333 bÀi ToÁn tÍch PhÂn Luy n

8/14/2019 333 bi Ton tch Phn Luy n

1/13

333BI TON TCH PHN LUYN THI I HC1/ Cho hm s : f(x)= x.sinx+x2 . Tm nguyn hm ca hm s g(x)= x.cosx

bit rng nguyn hm ny trit tiu khi x=kT 2/nh m hm s: F(x) = mx 3 +(3m+2)x2 -4x+3 l mt nguyn hm ca hm s:

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

3/Tm h nguyn hm ca hm s: f(x)= cos3

x.sin8x.

TNH :

4/I =3

2

4

3tg xdx

T

T

5/I =

42

6(2cotg x 5) dx

T

T

6/I =2

0

1 cos xdx

1 cos x

T

7/ I = 2

0

T

sin2 x.cos2xdx

8/I = 3

0

T

(2cos2 x-3sin2 x)dx

9 / I =2

2

s i n ( x )4 d x

s i n ( x )4

T

T

T

T

10 / I =

3

6

T

T (tgx-cotgx)2

dx

11/ I =4

4

0

cos x dx

T

12 / I =2

3

0

sin x dx

T

13*/ I =3 32

3

sin x sin xcotgxdx

sinx

T

T

14/I =2

4

0

sin x dx

T

15/I = 3

4

22

2cos

2sin

1T

Txx dx

16/I = 4

6

cotg2x dx

17/I =22 sin x

4

e sin 2x dx

18/ I =

4

02

2

cos

xe

tgx

.

34/I =1

2 23

1dx

x 4 x


2/13

19/ I = 2

4

4sin

1T

T xdx

20/ I = 4

0

6cos

1

xdx

21/I = dxxxnsix )cos(2cos44

2

0

T

22/ I =2

3

0

cos xdx

T

23/ I =32

0

4sin xdx

1 cosx

T

24/ I =1

3 2

0

x 1 x dx

25/I =1

5 2

0

x 1 x dx

26/I =1

0

xdx

2x 1

27/I =

1

x0

1

dxe 4

28/I =2

x1

1dx

1 e

29/I =2x2

x0

edx

e 1

30/I =x1

x0

edx

e 1

31/I =e

21

ln x dxx(ln x 1)

32/I =

7

3

30

x 1dx

3x 1

33/I =2

3 2

0

(x 3) x 6x 8 dx

.

35/I =4

22

1dx

x 16 x

36*/I =6

22 3

1dx

x x 9

37/I =2

2 2

1

x 4 x dx

38/I =2

2 3

0

x (x 4) dx

39/I =24

4 33

x 4dx

x

40*/I =22

22

x 1dx

x x 1

41/I =ln 2

x

0

e 1dx

42/I =1

0

1dx

3 2x

43/I =2

5

0

sin xdx

T

44*/I =3

0

1 dxcosx

T

45/I =2x1

x0

edx

e 1

46/I =ln3

x0

1dx

e 1

47/I =

4

2

6

1

dxsin x cot gx

T

T

48/I =3 2e

1

ln x 2 ln xdx

x

.


3/13

49/I =e

1

sin(ln x)dx

x

50/I =1

3 4 5

0

x (x 1) dx

51/I =

12 3

0 (1 2x)(1 3x 3x ) dx

52/I =2

31

1dx

x 1 x

53/I =3

2 2

6

tg x cot g x 2dx

54/I =1

2 3

0

(1 x ) dx

55*/I =1

2x0

1dx

e 3

56/I =xln3

x 30

edx

(e 1)

57/I =0

2x 3

1

x(e x 1)dx

58/I =2

6 3 5

0

1 cos x sin x.cos xdx

59*/I =2 3

25

1dx

x x 4

60/I =4

0

xdx

1 cos 2x

61/I =

2xln5

xln 2

e dxe 1

62/I =2e

1

x 1.ln xdx

x

63/I =21

0

xdx

(x 1) x 1

64/I =2

0

sin x.sin2x.sin3xdx

65/I =2

4 4

0

cos 2x(sin x cos x)dx

66*/I =2

3 3

0

( cos x sin x )dx

67/I =73

8 42

xdx

1 x 2x

68*/I =2

0

4cos x 3sin x 1dx

4sin x 3cos x 5

69/I =

9

31

x. 1 xdx

70/I =2

30

x 1dx

3x 2

71*/I = 6

0

xsin dx

2

72*/I =2

0

xdx

2 x 2 x

73/I =3 3 2

0

x . 1 x dx

74**/I =1

20

ln(1 x)dx

x 1

75/I =2

0

sinxdx

sin x cos x

76/I =

e

1 cos(ln x)dx

77*/I =2

2

0

4 x dx

78/I =2

1

xdx

1 x 1

.


4/13

79/I =e

1

1 3ln x ln xdx

x

80/I =3

2

2

ln(x x)dx

81/I =

e2

1(ln x) dx

82/I =

2e

e

ln xdx

x

83/I =

2e

1

ln xdx

ln x

84/I =2

2

1

x ln(x 1)dx

85/I =3

23

1 dxx 3

86/I =1

20

1dx

4 x

87/I =

2

4

0

sin xdx

88/I =3

2

6

ln(sin x) dxcos x

89/I =2

1

cos(ln x)dx

90*/I =2

2

0

ln( 1 x x)dx

91*/I =3

22

1dx

x 1

92/I =38

1

x 1dx

x

93/I =33

21

xdx

x 16

.

94/I =6

20

cosxdx

6 5sin x sin x

T

95*/I =

2e

2e

1 1( )dx

ln xln x

96/I =

32

4 x 4 dx

97/I =2

3 2

1

x 2x x 2 dx

98/I =

34

4

cos 2x 1dx

T

T

99/I =0

cos x sin xdxT

100/I =2

0

1 sin xdxT

101/I =

34

4

sin 2x dx

T

T

102/I =

0

1 sin xdxT

103/I =1 3

2

1

ln(x x 1) dx

-

104*/I =2

0

xsinxdx

1 cos x

T

105*/I =1

2 x1

1dx

(x 1)(4 1)

106*/I =41

x1

xdx

1 2

107/I =

2

4

0

x sin xdx

T

108/I =

2

4

0

x cos xdx

T


5/13

109/I =6

2

0

x.sin x cos xdx

T

110*/I =2 x1

20

x edx

(x 2)

111/I =2x 2

0 e sin xdx

T

112/I =2

2

1

1x ln(1 )dx

x

113/I =e

21e

ln xdx

(x 1)

114/I =

12

0

1 xx.ln dx

1 x

115/I =2t

1

ln xdx I 2

x

116/I =3

0

sin x.ln(cosx)dx

T

117/I =2e 2

1

cos (ln x)dx

T

118/I =4

0

1dx

cosx

T

119*/I =4

30

1dx

cos x

T

120/I = 21

3 x

0x e dx

121/I =22 sin x 3

0

e .sin x cos xdx

T

122/I =2

40

sin2xdx

1 cos x

T

123/I =1

20

3dx

x 4x 5

124/I =2

21

5dx

x 6x 9

125/I =1

2

5

1dx

2x 8x 26

126/I =1

0

2x 9dx

x 3

127/I =4

21

1dx

x (x 1)

128*/I =0

2

2

sin2xdx

(2 sin x)T

129/I =1

20

x 3dx

(x 1)(x 3x 2)

130/I =1

30

4xdx

(x 1)

131/I =1

4 20

1dx

(x 4x 3)

132/I =

33

20

sin xdx(sin x 3)

T

133/I =33

6

4sin xdx

1 cos x

T

T

134/I =3

2

6

1dx

cosx.sin x

T

T

135/I =3

0

sin x.tgxdx

T

136/I =3

4

1dx

sin2x

T

T

.


6/13

137/I =34

2 2 50

sin xdx

(tg x 1) .cos x

T

138/I =3

2 2

3

1dx

sin x 9cos x

T

T

139/I =2

2

cos x 1dx

cos x 2

T

T

140/I =2

0

1 sin xdx

1 3cos x

T

141/I =

2

0

cosx

dxsin x cos x 1

T

142/I =4

21

1dx

x (x 1)

143/I =1

33

1dx

x 4 (x 4)

144/I =33

0

sin xdx

cosx

T

145/I =1

0

x 1 xdx

146/I =6

4

x 4 1. dx

x 2 x 2

147/I =0

21

1dx

x 2x 9

148/I =3

21

1dx

4x x

149/I =2

2

1

4x x 5 dx

150/I =2

22

2x 5dx

x 4x 13

151/I =1

x0

1dx

3 e

152/I =

14x 2x2

2x0

3e edx

1 e

153/I =4

27

1dx

x 9 x

154/I = 2 x 2

0

e sin xdx

T

155/I =42

4 40

cos xdx

cos x sin x

T

156/I =1

0

3dx

x 9 x

157/I =0xsinxdx

T

158/I = 2 2

0

x cos xdxT

159/I =1

0

cos x dx

160/I =1

0

sin x dx

161/I =

2

4

0

x sin x dx

T

162/I =

2

4

0

x cos x dx

T

163/I = 2

0

xcos xsin xdxT

164/I =6

2

0

xcos xsin xdx

T

165/I =4

x

1

e dx

166/I =4

3x

0

e sin 4x dx

T


7/13

167/I = 2x 2

0

e sin x dxT

168/I =2 x1

20

x edx

(x 2)

169/I =e

1

(1 x) ln x dx

170/I =e

2

1

x ln x dx

171/I =

1

e2

1

ln x dx

172/I =e

1

x(2 ln x) dx

173/I =

2e

2e

1 1( )dxln xln x

174/I =2

2

1

(x x) ln x dx

175/I =2

2

1

1x ln(1 )dx

x

176/I =2

51

ln xdx

x

177/I =e

21e

ln xdx

(x 1)

178/I =

12

0

1 xx ln dx

1 x

179/I =2

3

cos x.ln(1 cos x)dx

T

T

180/22 sin x 3

0

e sin x cos x dx

T

181/I=2

40

sin2xdx

1 sin x

T

.

182/I =2

40

sin2xdx

1 cos x

T

183/I =2

21

5dx

x 6x 9

184/I =

21

0

x 3x 2

dxx 3

185/I =4

21

1dx

x (x 1)

186/I =1

20

ln(1 x)dx

x 1

187/I41

60

1 xdx

1 x

188/I =1

15 8

0x 1 x dx

189/I =x1

x x0

edx

e e

190/I=e

1e

ln x dx

191/I =2

sinx

0(e cos x)cos x dx

T

192/I =2

0

sin2x.cosxdx

1 cos x

T

193/I =2

0

sin 2x sin xdx

1 3cos x

T

194/I = 24

0

1 2sin x dx1 sin 2x

T

195/I =5 33

20

x 2xdx

x 1

196/I =3

2

4

tgxdx

cos x 1 cos x

T

T


8/13

197/I =2

2

1

x 1( ) dxx 2

198/I =4

2

0

x.tg xdx

T

199/I =

5

3( x 2 x 2 )dx

200/I =4

1

2dx

x 5 4

201/I =2

1

xdx

x 2 2 x

202/I =2

21

ln(1 x)dx

x

203/I =2

0

sin2xdx

1 cos x

T

204/I =20082

2008 20080

sin xdx

sin x cos x

T

205/I =2

0

sin x.ln(1 cosx)dx

T

206/I =23

21

x 1dx

x

207/I =34

20

sin xdx

cos x

T

208/I =2

2

0

cos x.cos4xdx

T

209/I =1

2x x0

1dx

e e

210/I =e

21e

ln xdx

(x 1)

211/I =1

0

1dx

x 1 x

212/I =21

20

xdx

4 x

213/I =1

20

xdx

4 x

214/I =

142

20

x

dxx 1

215/I =2

0

sin3xdx

cos x 1

T

216/I =

222

20

xdx

1 x

217/I =22

41

1 xdx

1 x

218/I =37

3 20

xdx

1 x

219/I =xln 2

x0

1 edx

1 e

220/I =1

0

x 1 x dx

221/I =1

2

0

x 1dx

222/I =2

3 3

0

(cos x sin x)dx

T

223/I =23

0

x 1dx

x 1

224/I =

1

2 2x0(1 x) .e dx

225/I =2

20

cosxdx

cos x 1

T

226/I =

7

3

30

x 1dx

3x 1

.


9/13

227/I =2

6

1 sin 2x cos 2xdx

cos x sin x

T

T

228/I =x 21

2x0

(1 e )dx

1 e

229/I = 3 2 3

0

x (1 x) dx

230/I =32

20

sin x.cos xdx

cos x 1

T

231/I =

12

20

4x 1dx

x 3x 2

232*/I = 20

xsin x.cos xdx

T

233/I =2

0

cosxdx

cos 2x 7

T

234/I =4

21

1dx

x (x 1)

235/I =

22 3

0 sin 2x(1 sin x) dx

T

236/I =2

30

x 1dx

3x 2

237/I =4

27

1dx

x x 9

238/I = 3 4

0

x sin x cos xdxT

239/I =2 3

2

cos x cos x cos xdx

T

T

240*/I =1

2

1

ln( x a x)dx

241/I =2

x0

1 sin xdx

(1 cos x)e

T

242/I =2

0

sin 2x sin xdx

cos3x 1

T

243/I =4

2 2

0

sin2xdx

sin x 2cos x

T

244/I =

232

20

xdx

1 x

245/I =

232

20

xdx

1 x

246/I =21

2

22

1 xdx

x

247/I =21

20

xdx

4 x

248/I =2

22

3

1dx

x x 1

249/I =1

5 3 6

0

x (1 x ) dx

250/I =2

0

sinxdx

1 sin x

T

251/I =2

0

cosxdx

7 cos 2x

T

252/I =4

21

1dx

(1 x)x

253/I =2

30

x 1dx

3x 2

254*/I =3

4

cos x sin xdx

3 sin 2x

T

T

.


10/13

255/I =2

3

2

cos x cos x cos xdx

T

T

256/I =3

4

4

tg xdx

T

T

257*/I =2

x

0

1 sin xe dx

1 cos x

T

258/I =1

2 3

0

(1 x ) dx

259/I =4

2

0

x.tg xdx

T

260/I=2

2 20

1dx

(4 x )

261/I =21

30

3xdx

x 2

262*/I =52

51

1 xdx

x(1 x )

263/I =3

20

cosx dx1 sin x

T

264/I =23

60

sin xdx

cos x

T

265/I =36

0

sin x sin xdx

cos2x

T

265/I =2

3

1dx

sin x 1 cos x

T

T

266/I =3

6 21

1dx

x (1 x )

.

267/I =2

20

sinxdx

cos x 3

T

268/I =

2

0

sin xdx

x

T

269/I = 2 2

0

sin xcos x(1 cos x) dx

T

270/I =4 44

0

sin x cos xdx

sin x cos x 1

T

271/I =4 44

0

sin x cos xdx

sin x cos x 1

T

272/I =2

0

sin x cos x cos xdx

sin x 2

T

273/I =

11 x

3a

edx

x

274/I =3 21

20

x 2x 10x 1dx

x 2x 9

275/I =31

2 30

x dx(x 1)

276/I =1

30

3dx

x 1

277*/I =41

60

x 1dx

x 1

278/I =1

3

0

xdx

(2x 1)

279/I =7

2

1dx

2 x 1

280/I =

32

21

2

1dx

x 1 x

.


11/13

281*/I =21

20

x ln(x 1 x )dx

1 x

282/I =4

2

1

(x 1) ln xdx

283/I =3

2

0

x ln(x 1)dx

284/I =32

21

3xdx

x 2x 1

285/I =1

3 20

4x 1dx

x 2x x 2

286/I =

12

21

2

1dx

(3 2x) 5 12x 4x

287/I =1

0

1dx

x 1 x

288/I =2

0

cosxdx

2 cos 2x

T

289/I =2

4

cos x sin xdx

3 sin 2x

T

T

290/I =2

3 3

0

(cos x sin x)dx

T

291/I =2

5 4

0

cos x sin xdx

T

292/I =2

4 4

0

cos 2x(sin x cos x)dx

T

293/I =2

0

1dx

2 sin x

T

294/I =2

0

1dx

2 cos x

T

295/I =2

22

3

1dx

x x 1

296/I =37

3 20

xdx

1 x

297*/I =

2

31

1 dxx 1 x

298/I =31

20

xdx

x 1 x

299/I =1

21

1dx

1 x 1 x

300/I =3

4

6

1 dxsin x cos x

T

T

301/I =2

0

cosxdx

cos x 1

T

302/I =2

0

cosxdx

2 cos x

T

303/I =2

0

sinxdx

sin x 2

T

304/I =32

0

cos xdx

cos x 1

T

305/I =2

0

1dx

2cos x sin x 3

T

306/I =2

2

3

cosxdx

(1 cos x)

T

T

307/I =4

3

0

tg x dx

T


12/13

.

308*/I =1

2x1

1dx

3 e

309*/I =2

x

sin xdx

3 1

T

T

310*/I =

2

0

sinx

dxcos x sin x

T

311/I =42

4 40

sin xdx

cos x sin x

T

312*/I =2

20

tgxdx

1 ln (cos x)

T

313*/I =2

0sinx dx

cos x sin x

T

314*/I =1

x 21

1dx

(e 1)(x 1)

315*/I =1

3x 1

0

e dx

316*/I =21

20

xdx

x 4

317*/I =32

4 20

cos xdx

cos 3cos x 3

T

318*/Tm x> 0 sao cho2 tx

20

t edt 1

(t 2)!

319*/I =3

2

4

tanxdx

cos x cos x 1

T

T

320*/I =1

2

0

3x 6x 1dx

321*/I =4

5

0

tg x dx

T

322/I =4

3

6

cotg x dx

T

T

323/I =3

4

4

tg x dx

T

T

324*/I =4

0

1dx

2 tgx

T

325/I =

52

0

sin x

dxcos x 1

T

326/I =3

2

6

cos2xdx

1 cos 2x

T

T

327*/I =4

2

0

t gx 1( ) dx

tgx 1

T

328*/I =

1

31

2

x dxx 1

329*/I =3 32

41

x xdx

x

330/I =xln3

x x0

edx

(e 1) e 1

331/I =

14e

21

e

1 dxx cos (ln x 1)

T

333*/I =4

0

ln(1 tgx)dx

T


13/13

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333 bÀi ToÁn tÍch PhÂn Luy n