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(1)333 BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC 1/ Cho hàm số : f(x)= x.sinx+x2 Tìm nguyên hàm hàm số g(x)= x.cosx biết nguyên hàm này triệt tiêu x=k 2/Định m để hàm số: F(x) = mx +(3m+2)x2 -4x+3 là nguyên hàm hàm số: f(x) = 3x2 +10x-4 3/Tìm họ nguyên hàm hàm số: f(x)= cos x.sin8x TÍNH : 4/I = 3tg x dx sin x dx 12 / I = sin x sin x 13*/ I = cot gx dx sin x 5/I = (2cotg x 5) dx 6/I = cos x cos x dx sin x dx 14/I = 0 x x dx sin cos 2 15/I = 7/ I = sin2 x.cos2xdx 8/I = (2cos2 x-3sin2 x)dx 9/ I= x) dx sin( x) 4 16/I = 17/I = esin x sin 2x dx 18/ 11/ I = cos x dx e tgx 2 I= cos x (tgx-cotgx)2 dx cotg2x dx sin( 10 / I = 34/I = Lop10.com x 4x dx (2) 35/I = 19/ I = sin x dx 36*/I = cos x dx 4 cos x(sin x cos x)dx 37/I = 22/ I = cos xdx 4sin x 23/ I = dx cosx x x dx 24/ I = 25/I = x x dx x dx 2x 1 27/I = x dx 0e 4 28/I = dx x 11 e e 2x dx 29/I = x e 1 e x dx 30/I = x 1 0e e ln x 31/I = dx x(ln x 1) 32/I = x2 dx x x 1 dx 3x 39/I = 3 40*/I = 2 ln 41/I = x2 1 dx x x 1 x e 1dx 42/I = 26/I = x x 9 dx 38/I = x (x 4)3 dx 2 x x dx dx 1 2 21/I = x 16 x 20/ I = 1 dx 2x 43/I = sin xdx dx cos x 44*/I = e 2x dx 45/I = x e ln dx 46/I = x e 1 47/I = sin x cot gx dx ln x ln x 48/I = dx x e 33/I = (x 3) x 6x dx Lop10.com (3) e sin(ln x) dx x 64/I = sin x.sin 2x.sin 3xdx 49/I = 50/I = x (x 1)5 dx 65/I = cos 2x(sin x cos x)dx 51/I = (1 2x)(1 3x 3x ) dx 52/I = 1 x 1x 3 66*/I = ( cos x sin x )dx dx x7 dx 67/I = x 2x 53/I = tg x cot g x 2dx 4cos x 3sin x dx 4sin x 3cos x 68*/I = 54/I = (1 x )3 dx 69/I = x xdx 1 55*/I = 2x dx e ln ex 56/I = x (e 1) x 1 dx 3x x 71*/I = sin dx 2 x 72*/I = dx x x 70/I = dx 57/I = x(e 2x x 1)dx 1 3 58/I = cos x sin x.cos xdx 73/I = 0 59*/I = x x 4 dx x 60/I = dx cos 2x e 2x dx x ln e e x 1 ln xdx 62/I = x 61/I = x2 63/I = dx (x 1) x 1 ln(1 x) dx x 1 ln x x dx 74**/I = sin x dx sin x cos x 75/I = e 76/I = cos(ln x)dx 77*/I = x dx x dx x 1 78/I = Lop10.com (4) 3ln x ln x 79/I = dx x e cos x dx 5sin x sin x 94/I = 80/I = ln(x x)dx e2 95*/I = ( e e 96/I = 81/I = (ln x) dx e 82/I = ln x dx x e e2 83/I = 97/I = x 2x x dx ln x dx ln x 98/I = 84/I = x ln(x 1)dx 85/I = 1 86/I = 4x cos 2x 1dx 99/I = cos x 100/I = dx 101/I = 88/I = cos x sin 2x dx 102/I = sin xdx dx 1 90*/I = ln( x x)dx x 1 x 1 92/I = dx x x3 dx 93/I = x 16 dx 103/I = ln(x x 1) dx 1 89/I = cos(ln x)dx 91*/I = sin xdx 3 sin xdx ln(sin x) sin xdx 2 87/I = 1 3 x dx x dx 4 2 1 )dx ln x ln x x sin x dx cos x 1 105*/I = dx x 1 (x 1)(4 1) x4 dx 106*/I = x 1 104*/I = 107/I = 2 x sin xdx 108/I = 2 x cos xdx Lop10.com (5) 109/I = x.sin x cos xdx x 2ex dx 110*/I = (x 2) 111/I = e 2x sin xdx x 112/I = x ln(1 )dx dx x 4x 5 124/I = dx x 6x 1 125/I = dx 2x 8x 26 5 2x 126/I = dx x 127/I = dx x (x 1) 123/I = e ln x dx (x 1) 113/I = e 128*/I = 114/I = x.ln 129/I = ln x 115/I = dx I x 116/I = sin x.ln(cos x)dx sin x 132/I = dx (sin x 3) e2 cos (ln x)dx 4sin x 133/I = dx cos x dx cos x 118/I = dx cos x.sin x dx cos x 134/I = 119*/I = x 3 dx (x 1)(x 3x 2) 4x 130/I = dx (x 1) 1 131/I = dx (x 4x 3) 1 x dx 1 x t 117/I = 3 x2 120/I = x e dx 121/I = e sin 2x dx (2 sin x) 135/I = sin x.tgxdx sin x .sin x cos xdx sin 2x 122/I = dx cos x 136/I = Lop10.com sin 2x dx (6) sin x 137/I = dx 2 (tg x 1) cos x 138/I = 152/I = 139/I = 140/I = cos x 1 sin x 156/I = cos x 141/I = dx sin x cos x 142/I = dx x (x 1) 1 3 x (x 4) sin x 144/I = dx cos x 0 158/I = x cos xdx dx 159/I = cos x dx 160/I = sin x dx 145/I = x xdx 161/I = x4 146/I = dx x x dx 147/I = 1 x 2x dx 148/I = 4x x 4x x dx 149/I = 1 150/I = 2 151/I = 2x x 4x 13 dx x 3 e dx x9 x 157/I = x sin xdx dx cos x 155/I = dx 4 cos x sin x 3cos x dx x 9x dx 143/I = 1 e 2x 154/I = e x sin xdx cos x dx 3e 4x e 2x 153/I = sin x 9cos x dx dx 2 x sin x dx 162/I = x cos x dx 163/I = x cos x sin x dx 164/I = x cos x sin x dx 165/I = e x dx 166/I = e3x sin 4x dx Lop10.com (7) 167/I = e 2x sin x dx x 2ex dx 168/I = (x 2) e 169/I = (1 x) ln x dx e 170/I = x ln x dx 1 e 171/I = ln x dx e 172/I = x(2 ln x) dx e2 1 )dx 173/I = ( ln x e ln x sin 2x dx cos x 183/I = dx x 6x 1 x 3x dx 184/I = x 185/I = dx x (x 1) ln(1 x) 186/I = dx x 1 1 x4 dx 187/I x 182/I = 188/I = x15 x dx 174/I = (x x) ln x dx x 175/I = x ln(1 ) dx ln x 176/I = dx x e ln x 177/I = dx (x 1) e 178/I = x ln 1 x dx 1 x 189/I = e e 190/I= e 191/I = (esin x cos x) cos x dx sin 2x.cos x dx cos x 192/I = sin 2x sin x dx 3cos x 2sin x dx sin 2x 194/I = x sin x cos3 x dx 195/I = sin 2x sin x dx dx ln x dx 180/ esin x 193/I = 181/I= x e 179/I = cos x.ln(1 cos x) dx ex 196/I = Lop10.com x 2x x 1 dx tgx cos x cos x dx (8) x 1 197/I = ( ) dx x 1 198/I = x.tg x dx 199/I = ( x x ) dx 3 dx 1 x x 201/I = dx x x 200/I = ln(1 x) 202/I = dx x sin 2x dx cos x x2 dx 212/I = x x 213/I = dx x 1 x4 214/I = dx x sin 3x dx cos x 215/I = 216/I = sin 2008 x 204/I = dx 2008 2008 sin x cos x dx 1 x 1 x2 dx 217/I = 11 x x3 218/I = dx 1 x ex dx 219/I = x e 0 ln 220/I = x x dx x2 1 dx x2 sin x 207/I = dx cos x 208/I = cos x.cos 4x dx 1 dx 2x ex 0e e ln x 210/I = dx (x 1) 209/I = e 205/I = sin x.ln(1 cos x) dx 206/I = x2 203/I = 2 211/I = dx x 1 x 221/I = x 1dx 222/I = (cos3 x sin x) dx x2 1 dx 223/I = x 1 224/I = (1 x) e 2x dx 225/I = 226/I = Lop10.com cos x cos x x 1 dx 3x dx (9) sin 2x cos 2x dx cos x sin x 227/I = (1 e x ) dx 228/I = 2x e sin 2x sin x dx cos3x 242/I = sin 2x dx 2 sin x 2cos x 243/I = 229/I = x (1 x)3 dx 230/I = 244/I = sin x.cos x 4x x 3x 231/I = 245/I = 246/I = 232*/I = x sin x.cos xdx 247/I = cos x 233/I = dx cos 2x 234/I = dx x (x 1) 248/I = x x2 dx cos x cos x cos xdx x3 1 x dx dx 1 x2 dx x2 x2 4x 2 dx x x 1 dx 250/I = 238/I = x sin x cos xdx 239/I = 1 x sin x dx sin x 236/I = x3 249/I = x (1 x )6 dx 235/I = sin 2x(1 sin x) dx 237/I = 2 x 1 dx 3x 2 2 dx cos x dx 2 240*/I = ln( x a x)dx 1 cos x dx cos 2x 252/I = dx (1 x)x x 1 253/I = dx 3x 251/I = cos x sin x dx sin 2x 254*/I = sin x 241/I = dx x (1 cos x)e Lop10.com (10) cos x cos x cos xdx 255/I = sin x dx cos x 267/I = 2 268/I = 256/I = tg xdx sin x 257*/I = cos x 269/I = sin x cos x(1 cos x) dx e x dx 258/I = (1 x )3 dx 259/I = x.tg xdx dx 2 (4 x ) 3x 261/I = dx x 2 x5 dx 262*/I = x(1 x ) 260/I= cos x dx sin x 263/I = sin x 264/I = dx cos x sin x sin x 265/I = dx cos 2x dx sin x cos x 265/I = 3 266/I = sin x dx x x (1 x ) dx sin x cos x 270/I = dx sin x cos x sin x cos x 271/I = dx sin x cos x sin x cos x cos x dx sin x 272/I = 273/I = ex dx x3 x 2x 10x dx 274/I = x 2x x3 dx 275/I = (x 1) 276/I = dx x 1 x 1 dx 277*/I = x 1 x 278/I = dx (2x 1) 279/I = dx x a 280/I = Lop10.com x 1 x dx (11) 281*/I = x ln(x x ) 1 x 295/I = dx 282/I = (x 1) ln x dx 296/I = 3x dx x 2x 1 4x 285/I = dx x 2x x 286/I = 287/I = 12x 4x x 1 x 298/I = 299/I = dx dx 290/I = (cos3 x sin x)dx 291/I = cos5 x sin xdx 292/I = cos 2x(sin x cos x)dx dx sin x 293/I = x 1 x x3 1 x dx dx x 1 x dx dx sin x cos x cos x dx cos x cos x dx cos x sin x dx sin x 303/I = cos3 x 304/I = dx cos x 305/I = 2cos x sin x dx cos x (1 cos x)2 dx 306/I = 294/I = dx cos x dx 300/I = 302/I = 1 x dx cos x sin x dx sin 2x 289/I = 1 301/I = x3 0x cos x dx cos 2x 288/I = x x 1 1 1 (3 2x) 2 297*/I = 2 283/I = x ln(x 1) dx 284/I = 2 307/I = tg x dx Lop10.com (12) 1 308*/I = dx 2x e 1 sin x dx 309*/I = x 321*/I = tg x dx 322/I = cotg x dx sin x 310*/I = dx cos x sin x 323/I = sin x dx cos x sin x 311/I = tgx 312*/I = ln (cos x) dx sin x 325/I = dx cos x sin x dx cos x sin x 1 314*/I = x dx (e 1)(x 1) 1 315*/I = e 316*/I = x cos 2x dx cos 2x 326/I = dx 327*/I = ( x 4 dx cos3 x 317*/I = dx cos 3cos x x t 2et dt 318*/Tìm x> cho (t 2) 319*/I = 1 tgx dx 313*/I = 3x 1 324*/I = tg x dx 4 tan x cos x cos x x dx x 1 328*/I = 2 329*/I = ln 330/I = dx 320*/I = 3x 6x 1dx x x 333*/I = ln(1 tgx)dx Lop10.com dx dx x cos (ln x 1) e x x3 dx x4 ex (e 1) e 1 e4 331/I = t gx ) dx tgx (13) Lop10.com (14)