333 BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC ➤TÍNH :

4/I =
3
2
4
3tg xdx
π
π
∫

5/I =
4
2
6
(2cotg x 5)dx
π
π
+
∫

6/I =
2
0
1 cosx
dx
1 cosx
π

s i n ( x )
4
π
− π
π
−
π
+
∫

10 / I =
∫
−
3
6
π
π
(tgx-cotgx)
2
dx

11/ I =
4
4
0
cos xdx
π
∫

12 / I =

15/I =
∫
3
4
22
2
cos
2
sin
1
π
π
xx
dx
16/I =
∫
4
6
π
π
cotg2x dx

17/ I =
2
2
sin x
4
e sin 2x dx
π
π

0
6
cos
1
π
x
dx

21/I =
dxxxnsix )cos(2cos
44
2
0
+
∫
π

22/ I =
2
3
0
cos xdx
π
∫

23/ I =
3
2
0
4sin x

dx
2x 1
+
∫

27/I =
1
x
0
1
dx
e 4
+
∫

28/I =
2
x
1
1
dx
1 e
−
−
∫

29/I =
2x
2
x

32/I =
7
3
3
0
x 1
dx
3x 1
+
+
∫

33/I =
2
3
2
0
(x 3) x 6x 8dx
− − +
∫

.
49/I =
e
1
sin(ln x)
dx
x
∫


tg x cotg x 2dx
π
π
+ −
∫

54/I =
1
2 3
0
(1 x ) dx
−
∫

34/I =
1
2 2
3
1
dx
x 4 x
−
∫

35/I =
4
2
2
1
dx


39/I =
2
4
4 3
3
x 4
dx
x
−
∫

40*/I =
2
2
2
2
x 1
dx
x x 1
−
−
+
+
∫

41/I =
ln 2
x
0

45/I =
2x
1
x
0
e
dx
e 1
−
−
+
∫

46/I =
ln3
x
0
1
dx
e 1
+
∫

47/I =
4
2
6
1
dx
sin x cotgx

x 3
0
e
dx
(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
π
−
∫

59*/I =
2 3
2

e
1
x 1
.ln xdx
x
+
∫

63/I =
2
1
0
x
dx
(x 1) x 1
+ +
∫79/I =
e
1
1 3ln x ln x
dx
x
+
∫

80/I =
3

∫

84/I =
2
2
1
xln(x 1)dx
+
∫

64/I =
2
0
sin x.sin2x.sin3xdx
π
∫

65/I =
2
4 4
0
cos2x(sin x cos x)dx
π
+
∫

66*/I =
2
3 3
0

x. 1 xdx
−
∫

70/I =
2
3
0
x 1
dx
3x 2
+
+
∫

71*/I =
6
0
x
sin dx
2
π
∫

72*/I =
2
0
x
dx
2 x 2 x

∫

76/I =
e
1
cos(ln x)dx
π
∫

77*/I =
2
2
0
4 x dx
+
∫

78/I =
2
1
x
dx
1 x 1
+ −
∫.

85/I =

6
ln(sin x)
dx
cos x
π
π
∫

89/I =
2
1
cos(ln x)dx
∫

90*/I =
2
2
0
ln( 1 x x)dx
+ −
∫

91*/I =
3
2
2
1
dx
x 1
−

x.sin xcos xdx
π
∫

110*/I =
2 x
1
2
0
x e
dx
(x 2)+
∫

111/I =
2x 2
0
e sin xdx
π
∫112/I =
2
2
1
1
x ln(1 )dx
x
+

( )dx
ln x
ln x
−
∫

96/I =
3
2
4
x 4 dx
−
−
∫

97/I =
2
3 2
1
x 2x x 2 dx
−
− − +
∫

98/I =
3
4
4
cos2x 1dx
π

π
−
∫

103/I =
1
3
2
1
ln(x x 1) dx
−
 
+ +
 
 
∫

104*/I =
2
0
xsin x
dx
1 cos x
π
+
∫

105*/I =
1
2 x

4
0
xcos xdx
π
∫114/I =
1
2
0
1 x
x.ln dx
1 x
+
−
∫

115/I =
2
t
1
lnx
dx I 2
x
 
⇒
<
 
 

0
1
dx
cos x
π
∫

120/I =
2
1
3 x
0
x e dx
∫

121/I =
2
2
sin x 3
0
e .sin xcos xdx
π
∫

122/I =
2
4
0
sin 2x
dx

139/I =
2
2
cosx 1
dx
cosx 2
π
π
−
−
+
∫

140/I =
2
0
1 sin x
dx
1 3cosx
π
+
+
∫

123/I =
1
2
0
3
dx

x 3
+
+
∫

127/I =
4
2
1
1
dx
x (x 1)
+
∫128*/I =
0
2
2
sin 2x
dx
(2 sin x)
−π
+
∫

129/I =
1
2

3
2
0
sin x
dx
(sin x 3)
π
+
∫

133/I =
3
3
6
4sin x
dx
1 cosx
π
π
−
∫

134/I =
3
2
6
1
dx
cosx.sin x
π

∫

142/I =
4
2
1
1
dx
x (x 1)
+
∫

143/I =
1
3
3
1
dx
x 4 (x 4)
−
+ + +
∫

144/I =
3
3
0
sin x
dx
cosx


148/I =
3
2
1
1
dx
4x x
−
∫

149/I =
2
2
1
4x x 5dx
−
− +
∫

150/I =
2
2
2
2x 5
dx
x 4x 13
−
−
+ +

e
1
(1 x)ln xdx
+
∫

170/I =
e
2
1
xln xdx
∫

171/I =
1
e
2
1
ln xdx
∫

152/I =
1
4x 2x
2
2x
0
3e e
dx
1 e

π
+
∫156/I =
1
0
3
dx
x 9 x
+ −
∫

157/I =
0
xsin xdx
π
∫

158/I =
2 2
0
x cos xdx
π
∫

159/I =
1
0

∫

164/I =
6
2
0
xcos xsin xdx
π
∫

165/I =
4
x
1
e dx
∫

166/I =
4
3x
0
e sin4xdx
π
∫

172/I =
e
1
x(2 ln x)dx
−

∫

176/I =
2
5
1
ln x
dx
x
∫

177/I =
e
2
1
e
lnx
dx
(x 1)
+
∫

178/I =
1
2
0
1 x
xln dx
1 x
+

∫.
197/I =
2
2
1
x 1
( ) dx
x 2
−
−
+
∫

198/I =
4
2
0
x.tg xdx
π
∫

199/I =
5
3
( x 2 x 2)dx
−
+ − −

∫

183/I =
2
2
1
5
dx
x 6x 9
− +
∫

184/I =
2
1
0
x 3x 2
dx
x 3
+ +
+
∫

185/I =
4
2
1
1
dx
x (x 1)

x 1 x dx
+
∫

189/I =
x
1
x x
0
e
dx
e e
−
+
∫

190/I=
e
1
e
lnx dx
∫

191/I =
2
sin x
0
(e cosx)cosxdx
π
+

π
−
+
∫

195/I =
5 3
3
2
0
x 2x
dx
x 1
+
+
∫

196/I =
3
2
4
tgx
dx
cosx 1 cos x
π
π
+
∫
∫

205/I =
2
0
sin x.ln(1 cosx)dx
π
+
∫

206/I =
2
3
2
1
x 1
dx
x
+
∫

207/I =
3
4
2
0
sin x
dx
cos x
π


211/I =
1
0
1
dx
x 1 x
+ +
∫

227/I =
2
6
1 sin 2x cos2x
dx
cosx sin x
π
π
+ +
+
∫

228/I =
x 2
1
2x
0
(1 e )
dx
1 e

dx
4 x
−
∫

213/I =
1
2
0
x
dx
4 x
−
∫

214/I =
1
4
2
2
0
x
dx
x 1
−
∫

215/I =
2
0
218/I =
3
7
3
2
0
x
dx
1 x
+
∫

219/I =
x
ln 2
x
0
1 e
dx
1 e
−
+
∫

220/I =
1
0
x 1 x dx


224/I =
1
2 2x
0
(1 x) .e dx
+
∫

225/I =
2
2
0
cosx
dx
cos x 1
π
+
∫

226/I =
7
3
3
0
x 1
dx
3x 1
+
+

∫

234/I =
4
2
1
1
dx
x (x 1)
+
∫

235/I =
2
2 3
0
sin 2x(1 sin x) dx
π
+
∫

236/I =
2
3
0
x 1
dx
3x 2
+
+

240*/I =
1
2
1
ln( x a x)dx
−
+ +
∫

241/I =
2
x
0
1 sin x
dx
(1 cosx)e
π
−
+
∫255/I =
2
3
2
cosx cosx cos xdx
π
π
−

cos3x 1
π
+
+
∫

243/I =
4
2 2
0
sin2x
dx
sin x 2cos x
π
+
∫

244/I =
2
3
2
2
0
x
dx
1 x
−
∫

245/I =

4 x
−
∫

248/I =
2
2
2
3
1
dx
x x 1
−
∫

249/I =
1
5 3 6
0
x (1 x ) dx
−
∫

250/I =
2
0
sin x
dx
1 sin x
π

+
∫

254*/I =
3
4
cosx sin x
dx
3 sin 2x
π
π
+
+
∫ .

258/I =
1
2 3
0
(1 x ) dx
−
∫

259/I =
4
2
0

dx
x(1 x )
−
+
∫

263/I =
3
2
0
cosx
dx
1 sin x
π
−
∫

264/I =
2
3
6
0
sin x
dx
cos x
π
∫

265/I =
3


.

281*/I =
2
1
2
0
xln(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
+
∫

∫

269/I =
2
2
0
sin xcosx(1 cosx) dx
π
+
∫

270/I =
4 4
4
0
sin x cos x
dx
sin x cosx 1
π
−
+ +
∫271/I =
4 4
4
0
sin x cos x
dx

1
2
0
x 2x 10x 1
dx
x 2x 9
+ + +
+ +
∫

275/I =
3
1
2 3
0
x
dx
(x 1)+
∫

276/I =
1
3
0
3
dx
x 1
+
∫


280/I =
3
2
2
1
2
1
dx
x 1 x−
∫

.

285/I =
1
3 2
0
4x 1
dx
x 2x x 2
−
+ + +
∫

286/I =
1
2
2
1
2

dx
3 sin 2x
π
π
+
+
∫

290/I =
2
3 3
0
(cos x sin x)dx
π
+
∫

291/I =
2
5 4
0
cos xsin xdx
π
∫

292/I =
2
4 4
0
cos2x(sin x cos x)dx

dx
3 e
−
+
∫

309*/I =
2
x
sin x
dx
3 1
π
−π
+
∫

310*/I =
2
0
sin x
dx
cosx sin x
π
+
∫

295/I =
2
2

298/I =
3
1
2
0
x
dx
x 1 x
+ +
∫

299/I =
1
2
1
1
dx
1 x 1 x
−
+ + +
∫
300/I =
3
4
6
1
dx

sin x 2
π
+
∫

304/I =
3
2
0
cos x
dx
cosx 1
π
+
∫

305/I =
2
0
1
dx
2cosx sin x 3
π
+ +
∫306/I =
2
2

312*/I =
2
2
0
tgx
dx
1 ln (cosx)
π
−
∫

313*/I =
2
0
sin x
dx
cosx sin x
π
+
∫

314*/I =
1
x 2
1
1
dx
(e 1)(x 1)
−
+ +

− +
∫

318*/Tìm x> 0 sao cho
2 t
x
2
0
t e
dt 1
(t 2)
=
+
∫

319*/I =
3
2
4
tan x
dx
cosx cos x 1
π
π
+
∫

320*/I =
1
2


324*/I =
4
0
1
dx
2 tgx
π
+
∫

325/I =
5
2
0
sin x
dx
cosx 1
π
+
∫

326/I =
3
2
6
cos2x
dx
1 cos 2x
π

2
4
1
x x
dx
x
−
∫

330/I =
x
ln3
x x
0
e
dx
(e 1) e 1
+ −
∫

331/I =
1
4
e
2
1
e
1
dx
xcos (ln x 1)

+++
=
63
0
3
11 xx
dx
I

336/
∫
−
=
3
3
ln
1ln2
e
e
dx
x
x
I

337/
(
)
∫
=
2

xex
xexx
I
x
x

.
340/
( )
∫
++
++=
1
0
12
2
12 dxexxI
xx

341/
( )
∫
+−
+−=

( )
∫
−
+−=
3
1
2013
23
23 dxxxI

344/
(
)
( )
∫
+−
+−
=
1
0
2
2
2
32
54
dx
xx
exx
I
x