333 BAI TOAN TICH PHAN HAY

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333 BAI TOAN TICH PHAN HAY

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(1)

LTĐH

333 BÀI TỐN 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 triệt tiêu x=k

2/Định m để hàm số: F(x) = mx3+(3m+2)x2 -4x+3 nguyên hàm hàm số:

f(x) = 3x2 +10x-4.

3/Tìm họ nguyên hàm hàm số: f(x)= cos3x.sin8x. TÍNH : www.giaoviengioi.com

4/I =

4

3tg x dx

5/I =

4

2

(2cotg x 5)dx

6/I =

0

1 cos x dx cos x

 

7/ I =2

0

sin2 x.cos2xdx

8/I = 3

0

(2cos2 x-3sin2 x)dx

9 / I =

2

sin( x)

4 dx

sin( x)

4 

 

  

10 / I = 

3

6

(tgx-cotgx)2 dx

11/ I = 4

cos x dx

12 / I =

sin x dx

13*/ I =

3

2

3

sin x sin x

cot gx dx sin x

14/I =

sin x dx

15/I = 

3

4

2

2 cos sin

1 

x x

dx

16/I = 4

6

cotg2x dx

17/I = sin x2

4

e sin 2x dx

18/ I = 4 

0

2

cos 

x etgx

(2)

LTĐH 19/ I = 

2

4

sin 

x

dx

20/ I = 4

0

cos 

x dx

21/I = 2cos2x(sin4x cos4 x)dx

 

22/ I =

cos xdx

23/ I =

0

4sin x dx cosx

24/ I =

1

3

0

x x dx

25/I =

1

5

0

x x dx

26/I =

1

x

dx 2x 1

27/I =

1 x

1 dx e 4

28/I =

2

x

1

dx e

29/I =

2x

x

e

dx e 1 

30/I =

x

x

e

dx

e

 

31/I =

e

2

ln x

dx x(ln x 1)

32/I =

7

3

x dx 3x

 

34/I =

1

2

3

1

dx x x

35/I =

4

2

1

dx x 16 x

36*/I =

6

2

1

dx x x  

37/I = 2

1

x x dx

38/I =

2

2

0

x (x 4) dx

39/I =

2 4

3

x

dx x

40*/I =

2

2

x

dx

x x

 

 

41/I =

ln x

e  1dx 

42/I =

1

1 dx

3 2x

43/I =2

sin xdx

44*/I =3

0

1 dx cos x

45/I =

2x

x

e

dx

e

 

46/I =

ln x

1

dx e 1 

47/I =

4

1

dx sin x cot gx

(3)

LTĐH 33/I =

2

3

0

(x 3) x  6x dx

.

49/I =

e

sin(ln x) dx x

50/I =

1

3

0

x (x  1) dx

51/I =

1

2

(1 2x)(1 3x 3x ) dx  

52/I =

2

3

1

dx x x

53/I =

3

2

6

tg x cot g x 2dx

 

54/I =

1

2

(1 x ) dx

55*/I =

1 2x

1 dx e 3 

56/I =

x ln

x

0

e

dx (e 1) 

57/I =

0

2x

1

x(e x 1)dx

 

58/I =26

0

1 cos x sin x.cos xdx

59*/I =

2

2

1

dx x x 4 

60/I =4

0

x

dx cos 2x

48/I =

3

e

ln x ln x dx x

.

64/I =2

0

sin x.sin 2x.sin 3xdx

65/I =2 4

0

cos 2x(sin x cos x)dx

66*/I =2 3

0

( cos x sin x )dx

67/I =

7

8

2

x

dx x  2x 

68*/I =2

0

4cos x 3sin x dx 4sin x 3cos x

 

 

69/I =

9

x xdx

70/I =

2

x dx 3x

 

71*/I =

0

x sin dx

2

 

72*/I =

2

x

dx x  x

73/I =

3

3

0

x x dx

74**/I =

1

ln(1 x) dx

x

 

75/I =2

0

sin x

dx sin x cos x

(4)

LTĐH 61/I =

2x ln

x ln

e

dx e  

62/I =

2 e

x

.ln xdx x

63/I =

2

0

x

dx (x 1) x 1 

79/I =

e

1 3ln x ln x dx x

80/I =

3 2

ln(x  x)dx

81/I =

e

2

(ln x) dx 

82/I =

2

e e

ln x dx x 

83/I =

2

e

ln x dx ln x 

84/I =

2

2

x ln(x 1)dx

85/I =

3

1 dx x 3 

86/I =

1

2

1

dx x

87/I =

2

4

sin xdx

88/I =

3

2

ln(sin x) dx cos x

89/I =

2

cos(ln x)dx 

76/I =e

1

cos(ln x)dx

77*/I =

2

2

4 x dx

78/I =

2

x

dx 1 x 1

.

94/I =6

2

cos x

dx 5sin x sin x

 

95*/I =

2

e e

1

( )dx

ln x ln x  

96/I =

3

x dx

97/I =

2

3

1

x 2x x dx

  

98/I =

3

4

cos 2x 1dx

99/I =

0

cos x sin xdx

100/I =

2

1 sin xdx

101/I =

3

4

sin 2x dx

102/I =

0

1 sin xdx

103/I =

1

2

ln(x x 1) dx

   

 

 

(5)

LTĐH 90*/I =

2

2

ln( x  x)dx

91*/I =

3 2

1

dx x  

92/I =

3

x dx x

93/I =

3

2

x

dx x  16 

.

109/I =6

0

x.sin x cos xdx

110*/I =

2 x

2

x e

dx (x 2)

111/I = 2x

0

e sin xdx

112/I =

2

1 x ln(1 )dx

x

113/I =

e

2

e

ln x dx (x 1)

114/I =

1

1 x

x.ln dx

1 x

 

115/I =

2 t

1

ln x

dx I

x

 

   

 

116/I =3

0

sin x.ln(cos x)dx

104*/I = 2

0

x sin x dx cos x

105*/I =

1

2 x

1

1

dx (x 1)(4 1)

  

106*/I =

4

x

x

dx

 

107/I =

2

4

x sin xdx

108/I =

2

4

x cos xdx

123/I =

1

3

dx x  4x 5

124/I =

2

5

dx x  6x 9

125/I =

1

1 dx

2x 8x 26

  

126/I =

1

2x dx x

 

127/I =

4

1

dx x (x 1)

128*/I =

0

2

sin 2x dx (2 sin x)

  

129/I =

1

2

x

dx (x 1)(x 3x 2)

  

130/I =

1

4x dx (x 1)

131/I =

1

4

0

1

(6)

LTĐH 117/I =e2

1

cos (ln x)dx

118/I =4

0

1 dx cos x

119*/I =4

3

1 dx cos x

120/I =

1 x

x e dx

121/I =2 sin x2 3

0

e sin x cos xdx

122/I =2

4

sin 2x dx cos x

137/I =

2

0

sin x

dx (tg x 1) cos x

138/I =

3

2

3

1

dx sin x 9cos x

 

139/I =

2

cos x dx cos x

 

 

140/I =

0

1 sin x dx 3cos x

 

141/I =2

0

cos x

dx sin x cos x

 

142/I =

4

1

dx x (x 1)

132/I =3

2

sin x dx (sin x 3)

133/I =

3

6

4sin x dx cos x

 

134/I =

3

2

1

dx cos x.sin x

135/I =3

0

sin x.tgxdx

136/I =

4

1 dx sin 2x

 

.

152/I =

1

4x 2x

2

2x

3e e

dx e

 

153/I =

4

2

1

dx x x

154/I = x

e sin xdx

155/I =

4

0

cos x

dx cos x sin x

156/I =

1

3

dx x 9  x 

157/I =

0

x sin xdx

(7)

LTĐH 143/I =

1

3

1

dx

x (x 4)

   

144/I =3

0

sin x dx cos x

145/I =

1

x xdx

146/I =

6

x

dx

x x

 

147/I =

0

1

dx

x 2x

  

148/I =

3

2

1

dx 4x x

149/I =

2

2

4x x dx

 

150/I =

2 2

2x

dx

x 4x 13

  

151/I =

1

x

1

dx e

167/I = 2x

0

e sin x dx

 

168/I =

2 x

2

x e

dx (x 2)

169/I =

e

(1 x)ln x dx

170/I =

e

x ln x dx

171/I =

1 e

2

ln x dx 

172/I =

e

x(2 ln x)dx

158/I = 2

0

x cos xdx

 

159/I =

1

cos x dx 

160/I =

1

sin x dx

161/I =

2

4

x sin x dx

162/I =

2

4

x cos x dx

163/I =

0

x cos x sin x dx

164/I =

x cos x sin x dx

165/I =

4 x

e dx

166/I =4 3x

e sin 4x dx

182/I =2

4

sin 2x dx cos x

183/I =

2

5

dx x  6x 9

184/I =

2

x 3x

dx x

  

185/I =

4

1

dx x (x 1)

186/I =

1

ln(1 x) dx

x

 

(8)

LTĐH 173/I =

2

e e

1

( )dx

ln x ln x  

174/I =

2

(x x)ln x dx

175/I =

2

1 x ln(1 )dx

x

176/I =

2

ln xdx x

177/I =

e

2

e

ln x dx (x 1)

178/I =

1

1 x

x ln dx

1 x

 

179/I =

2

3

cos x.ln(1 cos x)dx

180/2 sin x2 3

0

e sin x cos x dx

181/I=

4

sin 2x dx sin x

.

197/I =

2

2

x

( ) dx

x

 

198/I =4

x.tg x dx

199/I =

5

( x x )dx

  

200/I =

4

2

dx x

  

187/I

4

6

1 x dx x

 

188/I =

1

15

0

x x dx

189/I =

x

x x

0

e

dx e e

190/I=

e e

ln x dx 

191/I =2 sin x

(e cos x)cos x dx

192/I =2

0

sin 2x.cos x dx cos x

193/I =2

0

sin 2x sin x dx 3cos x

 

194/I =4

0

1 2sin x dx sin 2x

 

195/I =

5

3

x 2x

dx

x

 

196/I =3

2

tgx

dx cos x cos x

 

212/I =

2

2

x

dx x

213/I =

1

2

x dx x

214/I =

1

2

x

(9)

LTĐH 201/I =

2

x

dx x 2  x

202/I =

2

ln(1 x) dx x

203/I =2

0

sin 2x dx cos x

204/I =2 2008

2008 2008

0

sin x

dx

sin x cos x

205/I =2

0

sin x.ln(1 cos x)dx

206/I = 22

1

x

dx x

207/I =4

2

sin x dx cos x

208/I =2

cos x.cos 4x dx

209/I =

1

2x x

0

1

dx e e

210/I =

e

2

e

ln x dx (x 1)

211/I =

1

1

dx x 1  x 

227/I =

2

6

1 sin 2x cos 2x dx cos x sin x

 

228/I =

x

2x

(1 e ) dx e

 

215/I =2

0

sin 3x dx cos x

216/I =

2 2

2

x

dx x

217/I =

2

4

1 x dx x

 

218/I =

3

3

0

x

dx x

219/I =

x ln

x

1 e dx e

 

220/I =

1

x x dx

221/I =

1

x 1dx 

222/I =2 3

0

(cos x sin x)dx

223/I =

2

x

dx x

 

224/I =

1

2 2x

0

(1 x) e dx

225/I =2

2

cos x

dx cos x

226/I =

7

3

x dx 3x

 

.

242/I =2

0

sin 2x sin xdx cos3x

 

(10)

LTĐH 229/I =

3

2

0

x (1 x) dx

230/I =

2

sin x.cos x dx cos x

231/I =

1

2

4x dx

x 3x

  

232*/I =

0

x sin x.cos xdx

233/I =2

0

cos x

dx cos 2x

234/I =

4

1 dx

x (x 1)

235/I =2

0

sin 2x(1 sin x) dx

236/I =

2

x dx 3x

 

237/I =

4

2

1

dx x x 9 

238/I =

0

x sin x cos xdx

 

239/I =

2

cos x cos x cos xdx

 

240*/I =

1

2

ln( x a x)dx

 

241/I =2

x

1 sin x dx (1 cos x)e

 

243/I =4

2

0

sin 2x

dx sin x 2cos x

244/I =

2

2

x

dx x

245/I =

2

2

x

dx x

246/I =

2

2 2

1 x dx x

247/I =

2

2

x

dx x

248/I =

2

2

3

1

dx x x  

249/I =

1

5

0

x (1 x ) dx

250/I =2

0

sin x dx sin x

251/I =2

0

cos x

dx cos 2x

252/I =

4

2

1

dx (1 x)x

253/I =

2

x dx 3x

 

254*/I =3

4

cos x sin x dx sin 2x

 

(11)

LTĐH

255/I =

2

cos x cos x cos xdx

 

256/I =3

4

tg xdx



257*/I =2 x

0

1 sin x

e dx cos x

 

258/I =

1

2

(1 x ) dx

259/I =4

x.tg xdx

260/I=

2

2

1

dx (4 x )

261/I =

2

3

3x

dx x 2 

262*/I =

5

5

1 x

dx x(1 x )

 

263/I =3

2

cos x dx sin x

264/I =3

6

sin x dx cos x

265/I =6

0

sin x sin x dx cos 2x

265/I =

2

3

1

dx sin x cos x

 

267/I =2

2

sin x dx cos x

268/I =

2

0

sin x dx x

269/I =2

0

sin x cos x(1 cos x) dx

270/I =4 4

0

sin x cos x dx sin x cos x

 

271/I =4 4

0

sin x cos x dx sin x cos x

 

272/I =2

0

sin x cos x cos x dx sin x

 

273/I =

1 x a

e dx x 

274/I =

3

1

2

x 2x 10x

dx

x 2x

    

275/I =

3

2

0

x

dx (x 1) 

276/I =

1

3 dx x 1

277*/I =

4

6

x

dx

x

 

278/I =

1

3

x

dx (2x 1)

279/I =

7

1

dx x 1 

(12)

LTĐH

266/I = 6 2

1

1

dx x (1 x )

.

281*/I =

2

2

x ln(x x ) dx x

  

282/I =

4

2

(x 1) ln x dx

283/I =

3

x ln(x 1)dx

284/I =

3

2

3x

dx x 2x 1

285/I =

1

3

0

4x

dx

x 2x x

   

286/I =

1

2

2

1 dx

(3 2x) 12x 4x

   

287/I =

1

1

dx x  x

288/I =2

0

cos x

dx cos 2x

289/I =2

4

cos x sin x dx sin 2x

 

290/I =2 3

0

(cos x sin x)dx

291/I =2

0

cos x sin xdx

280/I =

3

2

2

1

dx x x

.

295/I =

2

2

3

1

dx x x  

296/I =

3

3

0

x

dx x

297*/I =

2

3

1

dx x x

298/I =

3

2

x

dx x x

299/I =

1

2

1

dx

1 x x

   

300/I =

3

1

dx sin x cos x

301/I =2

0

cos x dx cos x

302/I =2

0

cos x dx cos x

303/I =2

0

sin x dx sin x

304/I =2

0

cos x dx cos x

(13)

LTĐH

292/I =2 4

0

cos 2x(sin x cos x)dx

293/I =2

0

1

dx sin x

294/I =2

0

1

dx cos x

308*/I =

1

2x

1 dx e

 

309*/I =

2 x

sin x dx

3

  

310*/I =2

0

sin x

dx cos x sin x

311/I =2

4

0

sin x

dx cos x sin x

312*/I =2

2

tgx

dx ln (cos x)

313*/I =2

0

sin x

dx cos x sin x

314*/I =

1

x

1

1

dx (e 1)(x 1)

  

315*/I =

1

3x

e  dx 

316*/I =

2

2

x

dx x 4 

317*/I =2

4

0

cos x

dx cos 3cos x

 

305/I =

0

1

dx 2cos x sin x

 

306/I =

2

2

cos x

dx (1 cos x)

 

307/I =4

tg x dx

321*/I =4

tg x dx

322/I =4

6

cotg x dx

323/I =

4

tg x dx

 

324*/I =

0

1

dx tgx

325/I =2

0

sin x dx cos x

326/I =

3

2

cos 2x dx cos 2x

 

327*/I =4

0

t gx

( ) dx

tgx

 

328*/I =

1

(14)

LTĐH 318*/Tìm x> cho

2 t x

2

t e

dt (t 2) 

319*/I =3

2

tan x

dx cos x cos x

 

320*/I =

1

2

3x 6x 1dx

  

329*/I =

3

2

x x dx x

330/I =

x ln

x x

0

e

dx (e 1) e  

331/I =

1

e

2

e

1

dx x cos (ln x 1)

 

333*/I =4

0

ln(1 tgx)dx

(15)

LTĐH

Ngày đăng: 15/05/2021, 16:54

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