Bài tập tích phân chọn lọc

Tài liệu bao gồm gần 2000 bài tích phân của nhiều dạng khác nhau.

BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN BÀI TẬP TÍCH PHÂN    x dx 1. 2.  4.  cos x  sin x dx   3.  cos x cos xdx x  3x  dx    sin x sin xdx 5.   6.  sin x cos 3xdx cos x  1dx 10. 13.  x x  1 dx x 14. sin x  1dx 11.  x2 dx 2 x  4x  3 x  dx 26.  18. 22.  x  x2 1 x x2 1 dx 19. 23. 4x  0 x  dx 27.   sin  sin x  1 cos xdx 38. 20.  dx 2x 1  2x 1  x3 1 x 24. dx 2x 1 10 x  x  dx 1 x2 28. x 2x  dx 31.  x  5x  32.  x 2011  x 2011 dx  x 2011 x3 36. dx dx  4x  2011 35. x 12  1 dx  x 1  x  dx   x   x 1  x  dx 40 dx x 3 x dx 33.  x x 16.  x1  x 2010dx 64 x2 1 34.  dx x 1 dx 30.  x  x2 1 dx 29.  x 9 dx 15.  x x  1dx x  1dx x 2 e xln x dx 12.  x  x2  x  1 x 1 dx 3x  37.  25. 21. 8.  sin xdx   17. 7.  cos xdx  9.    x  cos xdx 39.  cos x  1.sin xdx  Hoàng Ngọc Phú Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN   40.  sin x cos xdx  41.  sin xdx   cos 42.  x  cos xdx   43.  sin x tan xdx 44. 46.  cos x cos x  cos xdx  45.  sin x 0 cos x dx dx  47. cos x  2 sin x  1    sin x 0 cos x  sin x dx 48. cos x  sin x  cos x  dx     tan x 49.  dx cos x dx 51.   tan x  tan x sin x dx 50.  sin x  52.  dx cot x  sin x    53. tan x e 0 cos x dx 54.    sin x  sin x cot xdx sin x 55. 57. dx  sin x 56. dx  cos x   sin x  cos x   sin x dx sin x cos x 0  cos x dx   58. 59. sin x cos x dx  cos x   sin x  sin x 0  cos x dx  sin x 0  sin x dx 60. 61.  dx  sin x  cos x 64. cos xdx 0 cos x  sin x  sin x 0 cos x dx 62.  63.    65. dx 0  sin x  66. sin xdx  3x   67.    tan xdx  cos x  cos x  68. sin xdx 0 sin x  cos x 69. sin xdx 0 sin x  cos x  sin xdx 0 sin x  cos x 70. Hoàng Ngọc Phú Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN   x  cos x dx  sin x  71.  72.  tan xdx ln e2x  e x 1 ln dx 76. 79.  dx  e2x 1  80. e x 1 x  1 x ln dx ln 88. e 1 x 2 91. dx  93.  x2 x dx 1 97. 1 2  dx x  2x  x 1 dx x4 1 x 1 x2 x 1 104.  ln 107.  4x  4 x 1 95. 1 dx  4x  102.   99.   dx  4x  4x dx x  x2 1 dx x  x dx  2x  x Hoàng Ngọc Phú 98.  dx 101.  dx 3 x4 1 0 x  1dx 94. dx  4x 2 103.    x dx  dx  2e  x  90.  x  x dx  3x dx x x e 85.  dx ln  ln  10  e  87. 82. dx  ln x ln xdx x e dx 1 x ln x  x x ln x   x  84. 81.  e2x e 106. e x  1.dx x  78. ex 1 ln  ln x 86.  dx x  ln x 100.  1  e  ln dx  77. dx e 96. 74. ln dx x e 1 dx 83.  x ln x ln ln x  e2 92. e  1.dx x e3 89. e 73. ln 2x ln 75. ln dx x x2  3 x 1 dx x  x2 1 105. dx x e  ex 108.  ln  e ln x2 1 dx x4  x2 1 ex x  1 e x 1 dx Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  e 109.  dx x ln x  x 110. dx x e 1 x2 1  1   111. sin x dx x3  cos  sin x 112.  dx cos x   113.  2 x  1sin xdx  114.  x1  cos x dx   115.  x   x cos xdx  x 117.  x  3e x dx  118. 116.  x cos xdx  e dx 2x 119.  x  32 x dx 121.  x ln x  1dx  x  e e dx 2 x x 3x  0 e x dx 125.   ln xdx 126.  ln x  x dx    x  sin x cos xdx 127.  3x 123. 124.  x ln x  1dx x 122.  x  e  dx 120. e 128.  x ln xdx  e 129. sin x   cos x cos xdx  xdx 0 cos x e e 130. 131. ln x 1 x dx 132. ln x  x  1 dx e  2 133.  e sin x sin x cos xdx 134.  cos x dx 135.  x sin x dx  136.  e sin 4xdx 3x Hoàng Ngọc Phú 137.  e dx x 138.  ln x  x  1 dx Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  139.  x cos x sin xdx  e 140.  cos ln x dx 141.   1  cos x dx sin x ln x  x e dx 142.  x  x 143.   cot   x  sin x dx sin x 144. sin x cos x dx x 1   cos     x  sin xdx   cos x  146.   1  x  xdx x 2 e  0 145.      147.   cos x   cos xdx sin x   0 149.  sin x cos xdx 148.  x ln 3x  1dx  e2 150.  x sin ln x dx 151. 153. 1 x dx 1 x  ln 156. e  154. x dx 152. 157.  x x  e2x ln  x  3dx 2 x  1 x  1  155. dx    dx  sin x x2 158. dx x5  2x3 x2 1 dx  tan x 0 cos x dx dx 0 cos x 159. 160. A   dx x 1  x 1  /2 161. B   /4   cos x.cos x dx 164. E   cos x(sin  2  x  cos x)dx /6 /6 165. F  x2  x  dx 2 x  /2  /2 163. D   162. C    cos x dx  /2  sin x dx 168. I   (| x  |  | x  |) dx 3 Hoàng Ngọc Phú 166. G   4sin xdx  cos x 167. H   | x  x  | dx 169. K   (| x  1|  | x |) dx 1 Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN   170. M      dx x  x2  /2  e 1/2 2/  176. R  x x 1 x2 179. U   4 x dx x 182. Y   ( x  2) dx 4 x 1 x dx 3 x 185. C   x4  dx x6  188. F   191. C   x 1 dx 3x  dx  /3 sin x  Hoàng Ngọc Phú /2 1 x  184. B   1 x dx 1 x 1  x  dx 187. E   10  x2  dx x4  x2  dx x 1 190. B   dx dx x 1 193. E   x dx ( x  1)3 x 3 1 x   x  dx  /2 197. I  198. K    cos x dx (sin x  cos x  3)3  /4 tan x dx 201. M   tan x dx 203. O    /3 200. L   /2 tan xdx x3 x2  dx x3 181. X   /4 202. N  dx 1 x2  x   dx sin x dx  sin x  x2 178. T    x dx 189. A   x x  dx  /2 199. I   186. D  195. G   7/3 196. H   /2 dx x x 4 194. F   183. A   192. D   3x  dx 4 x 4/ dx x  x2  180. V    1 x x2 175. R  dx 177. S   172. O   ln x x4 1 dx x2  174. Q   dx x x3 dx x8  173. P   171. N  /2 dx sin x  sin x dx  3cos x 204. P   x3  x dx Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN ln  205. Q   ex dx  ex dx 208. T   x  x3  /4 211. X     /2 /6  /2  /2  /2 S  ln 210. V     ln x dx  ln x ex dx (e x  1) 213. A    216. R   (cos3 x  sin x) dx ln x.  ln x dx x dx x  x 1  x2 dx x  x  12 ln e 218. E    /2 221. H   219. F  ln  ex   x ln x   /4 222. I   e2 x ex  cos x  sin x cos x dx  sin x e 224. L   dx sin x dx sin x  cos6 x  225. M   sin x sin x  sin x dx dx cos x.dx 13  10sin x  cos x  226. N   /2 215. C  x  3ln x .ln x dx x sin 3x dx  cos x  223. K   212. Y   cos3 x dx sin x   207. S  dx x x3  e dx x3 x 220. G  dx cos x 64 217. D  209. U   dx x  x 1  214. B   e x dx  x  1 206. R   227. O   dx  /4 cos x.cos  x    4    228. sin x dx sin x  cos x 2ln ex 1 ln  1 dx x e  x2    1 239. B   x ln 1   dx  x Hoàng Ngọc Phú    /2 237. Y  231. R   x2 1/2  dx  cos x 234. U  x2  2x  230. Q  dx 233. T   236. X   /2 dx  229. P   x  x2 232. S  x  x2 1  tan x dx cos x 5x2  dx x3  dx sin x dx sin x  cos6 x  240. C   x.sin x.cos x dx  /6 x.dx 235. V   238. A   x.ln( x  x  1)dx e 241. D   cos(ln x) dx Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  /2 242. E   ln( x  x)dx  243. F   /4 244. G  esin x sin x cos xdx  x tan xdx  e2  /2  245. H  e x cos xdx 248. L   x 2e x  x  2 dx e 251. O   x.ln x dx  sin x x e dx  cos x   246. I      dx ln x ln x  e  249. M      2 247. K   2  cos x dx 250. N   253. Q   ln( x   x )dx 252. P   ( x  x).e x dx ln ln( x  1) 254. R   dx ex  1 x3 dx 255.  x 1 x sin x dx 256. ex  (e x  1)3 dx  257.  x (e 2x 258.   cos x .sin x.cos xdx  x  1)dx 1 259.  dx x x2    2sin x dx 260.   sin x 261. x  x dx  x dx 262.   cos x 265.  x e dx x2 e 268.   ln x . ln x dx x Hoàng Ngọc Phú ln 263. x .  x dx 264. ln x2  ln xdx 266.  x e 269.  ln( x  x)dx  e2 x e 1 x dx 267. x 1  x  dx x4  x  dx 270.  x  Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  dx 271.  x  x 272. e cos x .sin xdx 273. 275.  x.  x dx 276. I   ln sin 2x  sin x  cos x sin 2x cos x dx 277. I    cos x 278. I   e sin x  279. I    cos x cos xdx   281. I    tan x  e 280. I   sin x tan xdx sin x 2 284.  (2 x  1) cos xdx 285. x3 287. I   1 x 1  x   289. I   e 3x sin 5xdx 290. I   cos 3x dx sin x  296. I   297. I   x ln xdx 298. I  294. I   sin x  2cos x.cos x 1 3x  dx  sin xdx x x sin xdx sin x cos x ; J   299. I   x sin xdx xdx x  13 301. I  dx x sin 2004 x dx 2004 x  cos 2004 x sin 302. I    ln x  sin x dx  cos x Hoàng Ngọc Phú 304.  x  2x  4x  dx x2   e  303. I   2 e  sin 2x ln x 293. I   dx x  295. I    291. I    sin x dx x  1.x dx e dx 292. I   1 x  2x  x .sin xdx 288. I   x  x dx dx  300. I    286. I   x . x  3dx dx  ln x dx 283.  x ln x  1 x 1 282. I   x ln xdx .cos x dx x2 e  dx   e3 x .sin xdx  2x x  e . e  1dx  ln 274. 2  sin x cos x  4sin x dx 305. e x dx  2e x  Page BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  dx 307. I   306.  ( x  2)e2 x dx 10 309.  ( x  2) ln xdx 2x   4x  313. I   ln 1  x  x2  x dx  x 316. I   315. I    sin x  cos x  3 321. I  ln  324. I   317. I   x ln  x2  5 dx dx  cos2x dx  2sin 2x 319. I    x  1 cos x dx 320. I   x 1  x   4sin3 x 322. I   dx  cos x dx x3 1 323. I   x dx cos2 x e  x3    ln x dx x  1 325. I   x.  x dx dx - ln x dx  ln x 314. I   x x2  1dx  e2x ex   dx x  sin 2x  cos2x 318. I   311. dx sin x  cos x  e x  x 1 312. I   xln 1+ x  dx dx 310. I   308.  ( x  1) sin xdx 326. I     327. I   x2  x3 dx  sin3x dx 330. I   cos3x  1 333. I    x  cos3 x  sin x dx    336. I    tg x dx e ln x  ln x dx x 339. I   Hoàng Ngọc Phú 328. I   2x  1 cos xdx   329. I   x e x  x  dx 331. I   x ln 1  x  dx x x 1 dx x5 332. I    cos x dx  2sin x 334. I   335. J    2x   ln  x  1 dx  sin3x  sin3 3x dx  cos3x 4x  dx x  3x  338. I   337. I      4 340. I   cos x  sin x dx  cos2x dx  2sin 2x 341. I   Page 10 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN ln 16  1421. I  1422. I  3e  4dx x ex  (e x  1)3 ln 1424. I  ln3 ln x e  1dx   x  4 x   1429. I  e2 dx x ln x.ln ex e log32 x x  3ln2 x dx  6e x  1431. I   x  ( x  2)ln x dx 1432. I   x (1  ln x ) e3 x e 1434. I  e2  e3 1436. I   1433. I  ln2 x  ln x  x2 ln( x   1) dx x 1 x 1 1437. I  e   ln x x  ln x xe  1439. I   dx x(e x  ln x) 1442. I   x ln x x 1 1440. I   e ln x3  ln x dx 1438.  x e dx 1446. I =   1   1448. I   x .ln  x   dx . x e 1451. I   ln x  e x (e x  ln x) .dx  ex Hoàng Ngọc Phú 1441. I   x ln( x  x  1)dx .sin xdx x  x ln x  x e dx 1443. I   x ln( x  1) dx x3 1445. I   s inx e dx dx x ln2 x  x ln x  dx 2 x (1  ln x ) e  dx 1435. I   dx ln x dx x  ln x e ex   dx  e e2 x ln e ln ln x 1427. I    ln x  ln2 x 1428. I   dx x 1430. I  14 e2 x   3x ln x  dx   x  ln x x dx x  3.6 x  2.4 x 1426. I   ln x  2 x e e 1423. I  1425. I   dx ln ln( x  1) x e    ln2 x  dx   x  ln x ln x 1444. I    dx 1 x   dx  1 x  1447. I   x ln  1449. I   x .ln(1  x )dx . 1450. I   ln x ( x  1) x 1452. I   ( x   )e x x dx dx Page 44 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN 1 0   x2 x  ex   x3  1455. I   x2  1457. I   ( x  1) 1459. I     dx   x 1456. I   e dx  1458. I  4 x x .e x 1 x2  dx 1460. I   ( x  1)ln x  x  dx 1461. I    x ln x 1462. I    x  x dx. dx   ln x  x   3x x2  e e3 ln3 x  ln x x x   dx 1 x   x2  e2 x . x x ln( x  1)  x 1454. I    x 2e x  1453. I   ln( x   x)dx dx dx  ln(5  x)  x3.  x dx x2 x sin x 1463. I   dx cos x 1464. I   ln x dx x 1 1465. I    x(2  x )  ln(4  x ) dx 1466. I   e x  x ln x  x e dx x  x2 ln xdx x 1467. I   1469. I  1468. I      x cos x  sin3 x 1470. I  dx  x sin x  cos3 x ( x  sin x) dx  sin x 1471. I   dx 1472. I    x(cos3 x  cos x  sin x )  cos x  1474. I  03 x  sin2 x dx  cos2 x   sin x x 1476. I   .e dx  cos x Hoàng Ngọc Phú dx 2 1473. I   x  ( x  sin x )sin x (1  sin x )sin2 x dx 1475. I   x  1sin x  1.dx  1477. I  02 cos x e x (1  sin x ) dx Page 45 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN   sin x  cos x  1478. I   6x   dx   sin xdx 1480. I  2 x   1482. I   ln(1  tan x )dx  cos(ln x )dx e  1481. I   esin x .sin x.cos3 xdx 1483. I   sin x ln(1  sin x )dx  1484. I   1479. I    tan x.ln(cos x ) dx cos x  1487. I     sin x 1 x  x dx 1485. Cho hàm số f(x) liên tục R f ( x)  f ( x)  cos4 x với x  R. 1486. Cho hàm số f(x) liên tục R f ( x)  f ( x)   cos2 x , với x  R. 1488. I   e  3x    x   x e x  x  1  x  dx 1489. I  x2  ( x sin x  cos x )2 dx .   1490. I   ln  sin x dx  cos x  sin x x e dx  cos x 1491. I    sin x dx 1492.  sin x  cos x  2 1493. I   sin sin x  nx dx  dx 1494. I      sin x sin  x   6  1495. I   x  sin x cos x  sin x cos x 1496. I   a cos x  b sin x cos x sin x  cos x   1497. I    1498. I   cos(    x)dx  1500. I   x  x dx Hoàng Ngọc Phú 16 1499. I    dx x 1 x x5  x3 dx 1501. I13   x2 1  e 1502. I16   dx x  ln x Page 46 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN   1502. I     sin x  cos x dx 6x  sin x dx sin x  cos x x sin x dx 1503.  cos x  1504. I   4x  dx 3x   1505. I1    1  1507. I3   lg 1   x   x dx     x 1506. I   lg 3 x  1000  x   dx 2 2004 1509. I   cos x.ln  x  1508. I    x  16  dx 1510. I6   ex  x  dx 4 x 7 x  x  16  n 1 dx 1 2000  1511. I   dx (e  1)( x  1) 1 sin x.sin x.cos x dx 2x  1512. I8     1513. I  sin x.sin x.cos x dx ex    1514. I10   x(tgx  cot gx)dx    x sin x dx cos x  1515. I11   1516. I12   1517. I13      3x  6x  1dx    sin x  cos x  1524.   1526.   ln (cos x)  cos3 x dx 1525.  cos  3cos x  x 4 dx tan x cos x cos x  x ln(x   x )  (e x  1)(x  1) dx 1  1528.  1523. dx sin x dx 1521.  x   1520.  dx 2x 1  e dx  tgx x 4sin x 1518. I14   cos x  sin x dx 1522. sin x dx sin x  cos x   1519. x dx 1527. Hoàng Ngọc Phú ex (e  1) e    1 x2 ln dx 1529.  x x dx cos x dx cos 2x  Page 47 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN x 2ex 1530.  dx (x  2)  1533.  sin 1531. x dx 1534. (3x  3)dx ( x  1)( x  3x  1) 1536.    x  ln  x  x   dx 1538.  x 1 1537.  cot x1  ln(sin x)dx   sin xdx 1539.  sin x  cos x (e x  e  x ) ln(e x  e  x ) dx e x  ex 1543.   x 2   1547.  x  s inx  x    dx cos x   x  dx e  ln x  1545.  x  x  ln x   dx  x   x    ln(1  x ) dx 1540.  x2 1 1541.  x 1 3  ( cos x  sin x )dx     (  cos2 x   cos2 x )dx 1542. 1544.  32 x  32 x  2dx 1  1546.  sin x(sin x  cos2 x)dx ( x3  3x  x  8)dx 1 x2  x  1548.  ( x  1)dx 1549.  3x   x    x  ln  x  x   dx 1550.  x2 1 1 2 x ln dx 1551.  1  x 2  x   e ln x1   ln x dx 1552.  x  cos x(1  sin x) 1553.  dx   sin x Hoàng Ngọc Phú ln(1  x)  x  dx 1532.    x x   1dx 1535.  x2 1  (x  1)(4x  1) dx 1  1554.  (1  sin x) n cos xdx (n  N ) Page 48 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN   sin   x  4 dx 1555.     sin   x  4   1556.   1558.  3ln x ln x dx x e  sin x.sin 2x.sin 3xdx 1560.   1561.   cos x sin x.cos xdx  1569. ln x  x(ln x  1)dx ln x  ln x dx x e 1557. e  ln(sin x)  cos x dx  1562.  cos x sin xdx 1565. 3 x   (x  4)  1567. sin e x 1564. sin x cos3 x dx dx 1 1566. 1569. sin x  cos x  1 e 2x dx  1568.  cos x.ln(1  cos x) dx  1571.    sin x  cos x  dx  3e4x  e2x   (x  1)(4x  1) dx  1563.  ln(x  x  1)  dx   1 tan x  ln (cos x) dx x ln( x   x ) 1573.  dx 2 (5 x  1)  x Hoàng Ngọc Phú 1570. cos x   cos x dx  /2 cos x  cos x 1572.  dx 4  sin x  cos x  4 sin x  1574.   cot x  dx   cos x  Page 49 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN dx 1575.  x  5x  2x  4dx 1577. x dx  10x 1576. 1578. x dx  13x dx  3x xdx 1 x 1579. x5  x dx 1581.  x 1 dx  x  x  19 x  22 1580. x 1582. dx  x 1 1583. xdx  x 1 1584. x dx  x 1 1585. x dx  x 1 1586. x dx  x 1 1587. x x   dx  5x  x  5x  dx  x2 1 1588. x 1591. x dx 1 1592. x xdx 1 1593. 1595. xdx  x 1 1596. x dx  x 1 1597. 1599. F1 =  1602.  xax 3x  5x + 7x   x + 2 b n x 99 dx  k  2x 1608. 7 x  199  2 x  1101dx 50 50  3 1603. 1606. 1609. x3 0 (1  x ) 1612. 1614.  x  x dx 1617.  1 e x x x xdx 1 1594. x x dx  x 1 1598. x dx  x 1 1601.  x2x dx  5x 100 dx Hoàng Ngọc Phú b  k dx dx x x2  e x dx 1616.  e  e  1 x 1613.  x  x dx x5 0 x  dx  10  7  3  x   x  3 x  5  dx 50 x19 dx 1610.  x(1  x)19 dx ln3 1618. n dx 1 10  x  5 dx 1607.  x  212 x n 1 dx  ax dx 1 1590. 1604. 2000 ex  3x 1  x dx  x1  x  1615. ln 1600. dx x 2000 dx 1605. 1611. 1589. xdx 1 1619.  x5  2x3 1 x2 dx  ln x dx 2x Page 50 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN    ln x ln x dx x e 1620.  1621.  cos x  sin x cos x. sin x dx 1622.   sin x sin x dx  1623. sin x 0 sin x  cos x dx 1624.  dx 0 ( x  1)( x  2) 1627.  1632.  sin x.ln(cos x )dx   sin x  cos x  ln x  ln 1637.    x ln x  e e dx 1635. 1  x  x  cos4 x )dx  x dx  1633.  1641.   x  x  x  x 1 cos x  1644.   (tan2 x  1)2 .cos5 x  e 1639.  ln x x2 dx ln x  ln(ln x ) dx x dx  dx 1642.    1 x   cos x.ln   x dx  1636. ln(ln x ) 1638.  dx x e2 sin3 x e3  ln( x  1)  x  dx  e2  ln2 x dx x  cos x ln( x   x )dx  ln x   x dx 1645. 1  1 x x dx  x2  1646.   cos2 x(sin   dx  1  sin x  sin xdx 1643. 1630.  1640.    1628. x2  2x  1 1629.  x x  x dx 1634. dx 1631. 1625.  x  x dx  x2 1626. x dx  1 x  sin x x2  Hoàng Ngọc Phú  dx 1647.    sin x  cos x dx  1648.    xdx  sin x Page 51 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  1649. x  cos x    1650.  sin x sin 3x cos 5xdx    sin x dx x2 1 dx x3  3x π 1653.   2cos2 xdx    x  sin x 0  sin2x dx 1654. 1651***.  x e x sin xdx  π 1652. 1655.  sin x.  cos x dx   1656.  sin 2 x.cos2 xdx 1657.  2sin xcos x   cos3 x  .sin xdx 0     sin x.  cos x dx  cos x  sin x x 0  cos x .e dx 1658.  2 1660. 1659.   x   x  sin x  sin x dx 1  sin x  sin x  1661.   dx 1662.     cos x.cos x    4  1663. 3sin x  4cos x 0 3sin x  4cos2 xdx   tan  x   4  0 cos x dx   1664. sin x . sin x  dx  7sin x  5cos x   sin x  cos x  dx 1665. Hoàng Ngọc Phú Page 52 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN      x dx 1666.  cos x    3sin x   1667.  sin x sin x  cos x  dx  e dx 1668.      sin x cos  x   6  1669. x 1670. x2 0  x  1  x2  x  dx 1672.  x3 x  0  x e   x dx    ln x  ln x   ln x  sin x sinx-sin x  1673.   e .sìn2x+ dx cos x   0  1674.   tan e x  tan x e x dx 1675. 1676.   ln x dx x 1 1677. x  x  3x dx 1679.  1 x  1 10 x  x   10 x  x  1 x   1681. 1 x 1  x2 dx cos x  2cot x  3cot x  1  sin x  dx .e  cot x sin x dx  1x  e x   1683.    x   tan x  dx   cos x  3 x      x tan dx x  .  1682.  2  1680.  ln x  1 x dx x  ln x  2 1678.   x  dx  5x  e x 0 x  2  2013e  x dx 1671. xdx Hoàng Ngọc Phú Page 53 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  1684. 2 x 1685. I  cos xdx x2  1687.    x  1 x  1 dx 1686. 1689. .e dx 3 ex  e x  2e x  x .e x 1693.  x 1x  1690.  1  x   e dx x 1 ln 1691.   x  2 dx 1692. e dx 1694. 1 x  1696. 1 x2   x ln x  dx x3  x 1 x2 x  cos x cos x  cos x  x 1698.  sin x   cos x 1  1  cos x   dx     sin x  xcos x  sin x   dx x sin x  cos x  1701.  x ln x  x  ln x      1 x ex 1 1 x  xe x ln e   e 1703. x  1699.  x   2ln x dx     1697. x  x 1  2ln x   ln x dx 1  ln  3x 1695.  x  x3  2014 x dx x4    1688. I  x.log x  dx x ln  ln x dx 1 x e x ln x  1700. sin x  dx   e 1702. ln xln x  1  ln x  x  1  dx   dx 1704.    cos x 1  1  cos x   x  21  xe x   1dx  x  xe x  ln x ln  x 1 x e  1705.  e  x2 1706.  x sin x  cos x  dx 1707.  e xe tan x tan x  1708.  cos x x x2   x3  x  1.3 x   1709.   x sin x dx cos x e2 x 2e x 1710.  dx x  4x  1711. ln x  ln x  x1  ln x  dx Hoàng Ngọc Phú Page 54 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  x5 0 x  x dx 1712.   1713. ln   dx x 1 1  x 1 ln 1714. x 1 ln  ln 1715. e ln e dx x  ex 1  1716. dx  x 1 ex 1  2x  10e  sin x  cos x   sin x  x e dx  cos x  0 sin xdx 1717.       x  1  sin x dx 4 1720.    sin x    1718.   x e x   x  dx  x  e 1719. ln x   x ln x  x dx  3 1721.     sin x  sin x dx sin x sin x  sin x cos x 0 sin x  cos x dx 1722. 1723. sin 3x  cos x cos x dx     xe x 4  sin x    sin x  4    dx 1724.  1  cos x    sin x 1726.  4 sin x  cos x 1727.  1733. 1736.  x ln x  x   dx x   1739***. 1742.  dx  4x  6x  7x  1738. dx  3x  27 3x  43  3 5 x Hoàng Ngọc Phú 1743. 5  x dx  3x 1746.  3x   2x    1744. 4 x  7dx  8  5x   5x  1747.  x dx 1  12 x  x x  dx dx 1741. x8 dx x4 1  xdx dx 1740.  2x  2x  x sin x  cos x  dx  x 1  4 x x 1735. 1734. x 1745. 1737. dx   dx dx  8x  ln sin x  cos x  0 cos x dx  2 x  1ln x 1732. 11 dx 1728.  e x x  x  1dx dx   sin x sin  x   6     x x 1730.  e x x  x  x  1dx 1731.  ln x  1  cos x e 1729.  e x x  x  1dx e  sin x 1725. 3x  x  dx   3x  x  3x  Page 55 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN 1748.  x2  dx x2  1751. x2 4  3x dx 1749.  4  x  x  2x  4x  2 x 1  x ln  xdx  1  x  1752. dx 2006 1753. x 2006 sin xdx 1  3 1754. 1750.  x1  3x 2008dx sin x  sin x dx sin x  sin 1755. x dx     x  dx 5 1756.   x  sin 2 x  1 4x   0  1757.  x sin x 1 2x dx  ln  ln x 1758.  dx x e  1759.  ln 1  tan x dx 2x  dx 1761.  x  x  x    1764. 1760. 1762.  x3 x dx sin x x x   cos xe dx    cos xe dx 1765. 1763.  x x8  1   dx x  1 sin x  cos x dx sin x  cos x dx  1766.  x x dx x   1767.  x     1769.  x1   ln x   ln x dx x    1 x2  1768.  x tan xdx dx  1770.  x x   3x  x ln dx 1 x  1771.  cos 3x  sin x  sin x e 1772.   sin x  16 cos x 0 sin x  cos x dx 1774.  cos x sin xdx x4 1777.  x  2x  1773.  1775. 1778.  x  2 1 ln x  ln x  1dx 1 xln x  1ln x  2 e x ln xdx 1 xln x  1ln x  2 2x  4x  1776. cos x  sin x  2 sin x  cos  dx dx 1779. x  x  3x   x x  3x  dx  x  sin x dx 1780.  x 1 1 Hoàng Ngọc Phú cos x dx 1781.  x 1 e  1782.   sin x sin x cos x dx ex 1 Page 56 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  1 x dx 1 2x x 1783.  dx x 1   1784. 1 1785.   x2 sin x dx 2x 1  1786.  1   sin x dx 1787.  6 sin x  cos x dx x e 1 x2 1  1788.  x sin x cos xdx  1789.  e x sin 3xdx 1790.  e x e dx x 11  cot 3x  dx 1792.  sin 3x 21 1795. 1797. 1800. 1803. sin 8x 5  tan 3x  tan 5x   sin 3x 7 dx cos 3x dx sin x cos x 10  cot x  dx 1806.  sin 5x 8 1798. dx tan x 2 dx  1812.  cos x 1815.  tan x  cot x dx cos x sin 8xdx  1820. K2   a dx 1799.  sin 5x cos 5x  sin 1804.  tan x  cot x dx 1805. tan 3x 7  cos 3x 6 tan x 4 dx  1813.  sin x sin 3xcos10xdx sin x  b cos x  3sin x  sin x  3sin x dx  cot 3x  1808.  sin 3x 41 1810. cos x 111 dx x cos x 1802.  sin x 3 Hoàng Ngọc Phú  sin x cos x dx sin x  sin x  cos x  2sin x  cos x dx 3sin x  4cos x  1819. K1  1801. sin 3x sin x 1817. F2    sin x cos 5x dx  tan x  dx 1807.  cos x 95 1809. 1796. tan x 20 dx  cos x 8  cot x  1794.  dx cos x 5  tan x  dx 1793.  cos x 3  sin 3x cos x dx  1791. 1811.  cos x cos 5x cos xdx 1814.  cos x sin 5xdx 1816. F1   4sin 3x  5cos 3x dx cos 3x  8sin 3x 1818. F3   4sin x  5cos x dx cos x  3sin x dx (với a  b ) dx 1821. I1   x3  x dx 1 Page 57 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  1822. I   32  x 1826.  x2 1 a x 1831.  x  x  2dx 1832. 1  1824. I   x3  32 1 x2  a2 dx x2 2a  1830. a  1 x2 1 dx x3 1833.  2x  x 1 2 x dx 2 x xdx  x  1 1827. x2  a2 dx x  1829.  x3 x   x1  x  2a x dx dx 1  dx  1823. I3  1828.  x3 x  1  x  dx 1825. dx x 1 x dx 1834. 1837.  1   1835.  3x  x dx 1838. x  x1  1843. x 1846.  1848.    x  1844. x  dx . x4 x4 1852. 1855. x  x 1   1 x  1853. dx  dx   dx  x 1   .  x   x  1 dx  x  a  x  b  1856. 1 x 1 x dx 1 x  n 1 n xdx  1  x  1 1 x 1  x  1  x  1   6    x 1  x 1 1850. x a  x  dx x2 xdx 1845. x 1 dx x 1 x 1  x  1x  1  x3 1842.   x ln x   x x  1 x 1866.  x sin ln x dx 1 x 1 x n 1 dx  1867.  x  2 1862.   1 x 8 e   x dx  cosln x dx 1865.  x ln xdx  x  x ln x ln x   x 1864. x e x dx 1 x  1861.  x ln  dx 1 x  Hoàng Ngọc Phú 1859. 1860.  x ln x  dx   x x  43 1858.  x sin x cos xdx  x sin xdx 1863. 1839. 33  x4  1847.  3 x 1   1849. dx x dx 2 1857. 1 x x  dx . x2 x2 1 dx dx 1836. dx  3 2 x . dx  x 2  x 2 1 x2 1 1841. dx 1 x 3 1854. x dx 1851. xdx dx x 8 x 1840. x  1 1868.  e x sin xdx Page 58 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN 1869.  e x  sin x dx  cos x a 1870.   a  x dx a  0 1871. sin x 0 e x dx  1872. dx  sin x 1873.  x5  2x x2 1 1874. dx  x3 dx x4    1876.  cos x ln 1  cos x dx 1875.  e sin x sin x cos xdx 1877.  sin x ln tan x dx     x  sin x 0  cos x dx 1878. 1879.  x dx 0 x sin x  cos x 2 dx 1880. tan x  cos x  sin x dx   ex  1882.  e   33 x  1881.  sin x cos sin x dx x  dx   1883.  x.32 x.4 x dx  e tan x  dx 1884.  cos x Hoàng Ngọc Phú 1885. Page 59 [...]...BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  1 2 343 I   342 I   sin x sin 2xdx 0 0 dx 2 1 x 1  ln x   2 e 348 I   sin 2x 1  sin x  dx 349 I   3 351 I   3 0 x2 3x  1 dx 1  x  1 dx 1  1  x 2 1  x   ... 3  2 e 345 I   x  2 tan x dx cos x  2 4 4  /2 xdx 3 2x  2 373 I   0 1 375 I   0 x3dx 4  x2 sin 2 xdx 3  4sin x  cos2 x 1  0  376 I    x.e2 x    dx 4  x2  x Page 11 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  3  ln x  x  12 dx 1 3 2 377  (cos3 x  1) cos 2 xdx 378 0 x 2  e x  2 x 2e x 380  dx 1  2e x 0 x sin x  ( x  1) cos x  x sin x  cos x dx 0 1  ln( x  1) dx x2 1 1  x... 0 409  1 382 I    2 x   ln xdx x 3 384 386 I   403 1 dx 1  4 400 x e ln xdx 381  x(2  ln x) 2 1  395 e 1 e 1 383 3 379  0 1 414 x2 1 dx x 1 dx  x 4  4x 2  3 0 Page 12 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN /3  415 /3 tg x  cot g x  2dx 2 2 dx sin x sin(x   / 6) /6  416 /6 / 4 sin 6 x  cos6 x dx 417  6x  1  / 4 3  420 2 2 421 1/ 9   0  0 424 I  1  1 /2  426 0  sin...  sin x)3 /3 428 x (10 4 2 x 1 dx 3 3x  1 3x 5  0 7/3 422 x2 1 x 1  x dx 5  418 ln(x  1) dx 439  0 x 2  2x  9 dx sin 4x dx sin x  cos6 x 6 1 443  x 5 (1  x 3 )6 dx 0 Page 13 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN 1 7 444  x 1  xdx  445 4 1x 2   449 (1  x) / 4 451 / 2 dx 448  1 x2 0 0 2 e 4 sin x cos xdx 452  454 0 x 1 dx 3 3x  1 1/ 2 (1  x) / 4  / 4 461  a cos x  b sin x 2 2... 1  cos x  dx x sin 2 3 473  tan 4 xdx  4 1 476  x 2  1dx 0 2 1 478  (1  x ) dx 2 3 0 10 481  x lg xdx 2 1 ln 3 482  0 x 2 sin x  / 2 479 I  / 2 1  2x  dx dx ex 1 Page 14 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN 2  x 2 2 483  xe dx 484 / 2  486  3 2 0 1/ 2 sin x 485 4  5x 4 0 1 cos x ln(x  1  x )dx / 4 xdx 1  490  11  x  / 2 1 x 1/ 3 b 495  (2x  1) x  1 a 496  x 2 2 x  a... 4sin 3 x 4 0 dx   xtg 488 6  (x  1)2 494 1 dx 487  4  sin x cos x 2 0 492 dx 1  cos x  3  / 2 489  2 2 dx 515  01  x  513  x sin 3 xdx 0  4 516  5e x sin 2 xdx 0 Page 15 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  / 2 4 2 cos xdx 517  3  2 sin x 0 518 3x 2  2 dx 519  2 x 1 1 4 522  0 520  1 528  (e x2 ln x 531  x2 1 0 1 1  526  1  x 2 arcsin xdx 3 2 0 t  2t  1 / 2  0 535  sin... 1 sin x  2 cos x  dx 0 (sin10 x  sin10 x  cos 4 x sin 4 x)dx 0 3    555  x sin xdx 0 553 x 0 4 x  11  5x  6 2   556  x 3 sin xdx 0 2 557 sin 2 x  1  sin 0 4 x dx Page 16 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN 1 558 1  0 1 561  xx  4 dx 20 562  564 0  0 567  x e 1 2x  / 4  0 1 x3 dx 565  2 x 1 0 0 1  2sin 2 x dx 1  sin 2x  573 1 /2  0   2 ex  1 x dx 1 1 x 1 577   /2... 0 0 5  1 1 559  e x sin 2 x dx xdx 2x  1 ln5 594 1 3  2 ln x dx x 1  2 ln x Hoàng Ngọc Phú 3 596  0 x5  2x3 x 1 2 dx dx x x 3 ln3 e  2e  3 dx 597   x2  x2  3 Page 17 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN 3 x4 2 598  x5  1 0 dx 599 1 2 601  x.sin xdx e3  603 0  (2x  1)cos2 xdx 0   3 607  ln x2  x dx 2  2 610   esin x  cos x  cos xdx    0 ex  1.e2x dx ln3 602 x 1 ... 2 x 631  dx 0 1  sin 2 x  3 tan x 617   cos x 1  cos2 x dx 4 620  1 x dx x x4 dx 5 1 0 x 2 623  1 626  x3 x2  3.dx 0  2 629  e3x sin5 xdx 0 0 632  dx 1 x2  2 x  4 Page 18 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN e ln x dx 633  1 x2  2 sin xdx 636  0 sin 2 x  2cos x.cos2 x 2 2 x3  2 x2  4 x  9 dx x2  4 0 639    7 3 x 1 634  dx 0 3 3x  1  3 x.sin 2 x 637  dx 2x 0 sin 2 x.cos 2 cos3x... 0 1  cos 2 x  3 663   cos x   Hoàng Ngọc Phú 1  dx x 1  x  4 1  2sin 2 x dx 661  0 1  sin 2 x 1 ln5 e2 x dx 662  ln2 e x  1 2 664  x3e x dx 0 2 665  x 2  x dx 0 Page 19 BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN  1 x2 666  dx ( x  1) x  1 0 2 667  sin x sin 2 x sin 3 xdx 0   2 668  cos 2 x(sin 4 x  cos 4 x)dx 0    2 669  cos5 xdx 0 3 x7 671  dx 21  x8  2 x 4 2 670  3 cos x  . BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN Hoàng Ngọc Phú Page 1 BÀI TẬP TÍCH PHÂN 1.   4 0 2 dxx 2.   3 0 2 23 dxxx 3.  4 0 cos2cos  xdxx .    2 0 3 cos1sin  xdxx 38.     6 0 3 cos5sin  xdxx 39.   2 3 sin.1cos6   xdxx BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN Hoàng Ngọc Phú Page 2 40.  2 6 32 cossin   xdxx 41.  2 0 3 sin  xdx .   2 0 cossin sin  xx xdx 69.   2 0 cos3sin sin  xx xdx 70.   2 0 44 4 cossin sin  xx xdx BÀI TẬP NGUYÊN HÀM -TÍCH PHÂN Hoàng Ngọc Phú Page 3 71. dx x xx     2 2 2 sin4 cos   72. dxx  4 0 5 tan 