333 bài toán tích phân 14 trang

‹ 333 BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC‹
1/ Cho hàm số : f(x)= x.sinx+x2 . Tìm nguyên hàm của hàm số g(x)= x.cosx
biết rằng nguyên hàm này triệt tiêu khi x=k π
2/Định m ñể hàm số: F(x) = mx 3 +(3m+2)x2 -4x+3 là một nguyên hàm của hàm số:
f(x) = 3x2 +10x-4.
3/Tìm họ nguyên hàm của hàm số: f(x)= cos 3 x.sin8x.
TÍNH :
π
3

π
2

4/I = ∫ 3tg 2 x dx

12 / I =

π
4
π
4

0

π
2 3

π
6
π
2 1 − cos x

3

π
2

4
∫ sin x dx

14/I =

∫ 1 + cos x dx

0

π
3

0

π
2

1
x
x dx
π sin 2
cos 2
4
2

2

∫

15/I =

7/ I = ∫ sin2 x.cos2xdx
0

π
3

8/I =

∫

π
4

(2cos2 x-3sin2 x)dx

16/I =

0

9/ I=

π
2

∫

− π
2

π
− x )
4
dx
π
s in (
+ x )
4
sin (

∫

−

π
6

∫

π
6

π
2

cotg2x dx

17/I = ∫ esin

2

x

sin 2x dx

π
4

π
3

10 / I =

sin 3 x − sin x
cot gx dx
∫
sin
x
π

13*/ I =

5/I = ∫ (2cotg 2 x + 5) dx

6/I =

3
∫ sin x dx

π
4

(tgx-cotgx)2 dx

18/

π
4

11/ I = ∫ cos 4 x dx

e tgx + 2
2
I= ∫
0 cos x

.

0

Xuct

om

ang web chuy˚n n hi

v

oŸn h c !

1


π
2

1

dx
x2 4 − x2
4
1
dx
35/I = ∫
2
2 x 16 − x
6
1
36*/I = ∫
dx
2
2 3 x x −9

1
19/ I = ∫ sin 4 x dx

π

3

4
π
4

1
∫0 cos 6 x dx

20/ I =
π
2

2

∫ cos 2 x(sin

21/I =

4

x + cos x)dx

2
2
∫ x 4 − x dx

37/I =

4

−1
2

0

π
2

38/I = ∫ x (x 2 + 4)3 dx

22/ I = ∫ cos3 xdx

0

0
π
2

∫

39/I =

4 3
3
− 2

1

−2
ln 2

1

41/I =

x
dx
26/I = ∫
2x
+
1
0
1
1
27/I = ∫ x
dx
e
+
4
0
2
1
28/I = ∫
dx
−x
1
−

e
1
2
e 2x
dx
29/I = ∫ x
0 e +1
1
e− x
dx
30/I = ∫ − x
+
e
1
0
e
ln x
31/I = ∫
dx
2
x(ln
x
+
1)
1

42/I = ∫

0
1

0
1

0
π
2

dx
x x +1
2

1
dx
3 − 2x

43/I = ∫ sin 5 xdx
0

π
3

1
dx
0 cos x

44*/I = ∫

e−2x
45/I = ∫ − x

dx
+
e
1
0
ln 3
1
46/I = ∫
dx
x
0
e +1
1

π
4

47/I = ∫

7
3

x +1
32/I = ∫
dx
3
3x
+
1
0

ang web chuy˚n n hi

x2 +1

x
∫ e − 1dx

25/I = ∫ x 5 1 + x 2 dx

om

∫

40*/I =

3
2
∫ x 1 − x dx

0

Xuct

x2 − 4
dx
x

4

4sin 3 x

23/ I = ∫
dx
0 1 + cosx
24/ I =

1

∫

34/I =

π sin
6

v

oŸn h c !

1
2

x cot gx

dx

2


2

ln x 3 2 + ln 2 x
48/I = ∫
dx
x
1
e

33/I = ∫ (x − 3) 3 x 2 − 6x + 8 dx
0

.

.

π
2

e

sin(ln x)
dx
x
1

49/I = ∫

64/I = ∫ sin x.sin 2x.sin 3xdx
0
π
2

1

50/I = ∫ x 3 (x 4 − 1)5 dx

65/I = ∫ cos 2x(sin 4 x + cos 4 x)dx

0
1

0

51/I = ∫ (1 + 2x)(1 + 3x + 3x 2 )3 dx
0
2

1

52/I = ∫

1+ x

1x
π
3

3

π
2

66*/I = ∫ ( 3 cos x − 3 sin x )dx

dx

0

x7
dx
67/I = ∫
8
4
2 1 + x − 2x
3

53/I = ∫ tg 2 x + cot g 2 x − 2dx

π
2

4cos x − 3sin x + 1
dx
4sin
x
3cos
x
5
+
+
0

π
6
1

68*/I = ∫

54/I = ∫ (1 − x 2 )3 dx

9

69/I = ∫ x. 3 1 − xdx

0

1

1
dx
2x
+3
0e
ln 3
ex

1
2

55*/I = ∫
56/I =

∫

(e + 1)
x

0

3

x +1
dx
3
3x
+
2
0
π
x
71*/I = ∫ sin 6 dx
2
0
2
x
72*/I = ∫
dx
2
+
x
+

2
−
x
0
70/I = ∫

dx

0

57/I = ∫ x(e 2x + 3 x + 1)dx
−1
π
2
6

3

58/I = ∫ 1 − cos3 x sin x.cos5 xdx

3
2
∫ x . 1 + x dx

73/I =

0

0

2 3

∫

59*/I =

5

π
4

1
x x2 + 4

ln(1 + x)
dx
2
x
+
1
0
1

74**/I = ∫

dx

π
2

sin x
dx
0 sin x + cos x

x
60/I = ∫
dx
0 1 + cos 2x
ln 5

61/I =

∫

ln 2

Xuct

om

75/I = ∫

eπ

e 2x

76/I = ∫ cos(ln x)dx

dx
e −1

x

ang web chuy˚n n hi

1

v

oŸn h c !

3


x2 +1
62/I = ∫
.ln xdx
x
1

2

e

77*/I = ∫ 4 + x 2 dx
0

2

x2
dx

(x
+
1)
x
+
1
0
1

x
dx
1 1 + x −1

78/I = ∫

63/I = ∫

.

1 + 3ln x ln x
dx
x

e

79/I = ∫

1
3

π
6

cos x
dx
2
6
−
5sin
x
+
sin
x
0

94/I = ∫

80/I = ∫ ln(x 2 − x)dx

e2

2

95*/I = ∫ (

e

e

81/I = ∫ (ln x) 2 dx

3

82/I = ∫
e

−4
2

ln x
dx
x

−1
3π
4

ln x
83/I = ∫
dx
ln x
1

∫ cos 2x + 1dx

98/I =

2

π

4
π

84/I = ∫ x ln(x 2 + 1)dx
1
3

99/I = ∫ cos x

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

85/I =

sin xdx

0

2π

100/I =

∫ 1 + sin xdx

0
3π
4

π2
4

101/I =

0
π
3 ln(sin x)

102/I = ∫ 1 − sin xdx

∫ sin xdx

88/I = ∫

cos 2 x

π
6
2

dx

0
1

π

x sin x
dx
2
0 1 + cos x
1
1
105*/I = ∫ 2
dx
x
−1 (x + 1)(4 + 1)

104*/I = ∫

2

90*/I = ∫ ln( 1 + x 2 − x)dx
0

ang web chuy˚n n hi

3

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

1

om

∫ sin 2x dx

π
4
π

89/I = ∫ cos(ln x)dx

Xuct

3
2
∫ x − 2x − x + 2 dx

97/I =

e2

87/I =

2
∫ x − 4 dx

96/I =

1

e2

1
1
−
)dx
2
ln x ln x

v

oŸn h c !

4


3

91*/I =

∫

x4
106*/I = ∫
dx
x
1
+
2

−1
1

1

2
2 x −1
8 3
x +1
92/I = ∫
dx
x
1
3
x3
dx
93/I = ∫ 2
1 x − 16

dx

π2
4

107/I =

∫ x sin xdx

0

π2
4

108/I =
.

∫ x cos xdx

0

π
6

1

3
dx
2
0 x − 4x − 5
2
5
124/I = ∫ 2
dx
1 x − 6x + 9
1
1
125/I = ∫
dx
2
−5 2x + 8x + 26

1
2x + 9
126/I = ∫
dx
x
+
3
0
4
1
127/I = ∫ 2
dx
x
(x
+
1)
1
123/I = ∫

109/I = ∫ x.sin x cos xdx
2

0

x 2ex
110*/I = ∫
dx
2
(x
+

2)
0
1

π

111/I = ∫ e 2x sin 2 xdx
0

2

1
x

112/I = ∫ x 2 ln(1 + )dx
1

e

ln x
dx
2
1 (x + 1)

113/I = ∫

0

128*/I =

e
1
2

2

1+ x
114/I = ∫ x.ln
dx
1
−
x
0

x −3
dx
2
(x
1)(x
3x
2)
+
+
+
0
1
4x
130/I = ∫ 3
dx
(x

+
1)
0
1
1
131/I = ∫ 4
dx
2
(x
+
4x
+
3)
0
1

129/I = ∫

2

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

π

3

116/I = ∫ sin x.ln(cos x)dx

π
3

0

π
e2

117/I =

sin 2x

dx
∫
2
−π (2 + sin x)

sin 3 x
dx
2
(sin
x
+
3)
0

132/I = ∫

2
∫ cos (ln x)dx

1

Xuct

om

ang web chuy˚n n hi

v

oŸn h c !

5


π
4

π
3

4sin 3 x
dx
133/I = ∫
π 1 − cos x

1
118/I = ∫
dx
0 cos x
π
4

6
π
3

1
dx
3
cos
x
0

119*/I = ∫
1

1
dx
2
π cos x.sin x

134/I = ∫

2

120/I = ∫ x 3e x dx
0
π
2

121/I = ∫ e

sin 2 x

6
π
3

135/I = ∫ sin x.tgxdx

3

.sin x cos xdx

0
π
3

0
π
2

136/I =

sin 2x
dx
4
+
1
cos
x
0

122/I = ∫

π
4

π
4

.

sin 3 x
137/I = ∫
dx
2
2
5
0 (tg x + 1) .cos x

152/I =

π

3

153/I =

−

139/I =

140/I =

cos x − 1

155/I =

1 + sin x

1

x + 4 + (x + 4)

dx

cos 4 x
∫ cos4 x + sin 4 x dx
0

156/I = ∫

cos x
141/I = ∫

dx
sin
x
cos
x
1
+
+
0
4
1
142/I = ∫ 2
dx
x
(x
+
1)
1
1
1
−3

2
7 x 9+x

dx

0
π
2

∫ 1 + 3cos x dx

∫

∫

1+ e
1

2x

154/I = ∫ e x sin 2 xdx

0
π
2

143/I =

∫

+ e 2x

π
2

∫ cos x + 2 dx
π
−

2
π
2

1
2 3e 4x
0
4

1
dx
138/I = ∫
2
2
π sin x + 9cos x
3
π
2

1

∫ sin 2x dx

0
π

3
dx
x+9 − x

157/I = ∫ x sin xdx
0
π

3

158/I = ∫ x 2 cos 2 xdx

dx

0
1

159/I = ∫ cos x dx
0

Xuct

om

ang web chuy˚n n hi

v

oŸn h c !

6


π

3

144/I = ∫

0
1

1

160/I = ∫ sin x dx

3

sin x
dx
cos x

0

π2
4

145/I = ∫ x 1 − xdx

0

x−4 1
.
dx
x

+
2
x
+
2
4
0
1
147/I = ∫
dx
2
−1 x + 2x + 9
3
1
dx
148/I = ∫
2
1 4x − x

π
4

2

146/I = ∫

162/I =

163/I = ∫ x cos 2 x sin x dx
0

π
6

164/I =

2
∫ 4x − x + 5 dx

−1
2

∫

150/I =

−2
1

151/I = ∫

0
π

2x − 5
x 2 + 4x + 13
1
dx
x
3+ e

165/I = ∫ e

dx

dx

166/I = ∫ e3x sin 4x dx
0
π
2

sin 2x
dx
4
+
1
cos
x
0
2
5
183/I = ∫ 2
dx
x
−
6x
+
9
1
1 2

x + 3x + 2
dx
184/I = ∫
x +3
0
4
1
185/I = ∫ 2
dx
1 x (x + 1)
1
ln(1 + x)
dx
186/I = ∫ 2
x
+
1
0
1
1+ x4
dx
187/I ∫
6
1
+
x
0
182/I = ∫

x 2ex

dx
2
(x
+
2)
0

168/I = ∫
e

169/I = ∫ (1 + x) ln x dx
1
e

170/I = ∫ x ln 2 x dx
1
1
e

171/I = ∫ ln 2 x dx
1
e

172/I = ∫ x(2 − ln x) dx
1

1

e2

188/I = ∫ x15 1 + x 8 dx

1
1
173/I = ∫ ( 2 −
)dx
ln x
e ln x

ang web chuy˚n n hi

x

1
π
4

0
1

om

2
∫ x cos x sin x dx

0
4

167/I = ∫ e2x sin 2 x dx

Xuct

∫ x cos x dx

0
π

2

149/I =

∫ x sin x dx

161/I =

0
6

0

v

oŸn h c !

7


2

1

2

189/I = ∫

1
175/I = ∫ x ln(1 + ) dx
x
1
2
ln x
176/I = ∫ 5 dx
1 x
e
ln x
dx
177/I = ∫
2
1 (x + 1)

178/I = ∫ x ln
0
π
2

190/I=

0
π
2

sin 2x.cos x
dx
0 1 + cos x

192/I = ∫

1+ x
dx
1− x

π
2 sin 2x

+ sin x
dx
1 + 3cos x

193/I = ∫

0
π
4 1 − 2sin 2

x
dx
1 + sin 2x

194/I = ∫
3

3

sin x cos x dx

π
2

∫

195/I =

0

181/I=

∫ ln x dx

0

180/ ∫ e

0

π
3

sin 2x

∫ 1 + sin 4 x dx

196/I = ∫

x −1 2
) dx
x+2

212/I = ∫

0

π
4
1

.

2

197/I = ∫ (
−1
π
4

0
5

dx

tgx
cos x 1 + cos x

2

dx

x4
214/I = ∫ 2
dx
0 x −1

−3
4

π
2

2
dx
∫
−1 x + 5 + 4
2
x
dx
201/I = ∫
1 x+2 + 2−x

200/I =

sin 3x
dx
+

cos
x
1
0

215/I = ∫

2
2

216/I =

∫

0

ang web chuy˚n n hi

x +1
2

1
2

199/I = ∫ ( x + 2 − x − 2 ) dx

om

x 5 + 2x 3

x2
dx
2
4
−
x
0
1
x
213/I = ∫
dx
2
0 4−x

198/I = ∫ x.tg 2 x dx

Xuct

dx

191/I = ∫ (esin x + cos x) cos x dx

π
3

sin 2 x

−x

1

e
π
2

179/I = ∫ cos x.ln(1 − cos x) dx
π
2

e +e
x

0
e

2

e
1
2

ex

1

174/I = ∫ (x 2 + x) ln x dx

v

oŸn h c !

x2
1− x2

dx
8


ln(1 + x)
202/I = ∫
dx
x2
1

1− x2
dx
217/I = ∫
4
1
+
x
1

2

2

π
2

sin 2x

dx
0 1 + cos x

218/I =

sin 2008 x
204/I = ∫
dx
2008
2008
+
sin
x
cos
x
0

219/I =

0
1

0

221/I = ∫ x 2 + 1dx

x +1
dx
x2
2

0
π
2

1
π
4 sin 3

222/I = ∫ (cos3 x + sin 3 x)dx

x
dx
0 cos x

207/I = ∫

0
3

x2 +1
223/I = ∫
dx
0 x +1

2

π
2

208/I = ∫ cos 2 x.cos 4x dx

1

224/I = ∫ (1 + x) 2 .e 2x dx

0
1

0
π
2

1
209/I = ∫ 2x
dx
x
e
+
e
0
e
ln x
210/I = ∫
dx
2
1 (x + 1)
e
1

211/I = ∫

π
6
1

0
7
3

226/I = ∫

1
dx
x +1 + x

0

x +1
dx
3
3x + 1

242/I = ∫

0
π
4

+ sin x

dx
cos3x + 1

sin 2x
dx
2
+
sin
x
2cos
x
0

243/I = ∫

2
2

229/I = ∫ x 2 (1 − x)3 dx
0

244/I =

∫

0

ang web chuy˚n n hi

dx

π
2 sin 2x

+ cos 2x
dx
cos x + sin x

3

om

cos x + 1
2

.

(1 + e x ) 2
228/I = ∫
dx
2x
1
+
e
0

Xuct

cos x

225/I = ∫

0
π
2 1 + sin 2x

227/I = ∫

dx
1+ x2
1 − ex
dx
1 + ex
3

220/I = ∫ x 1 − x dx

205/I = ∫ sin x.ln(1 + cos x)dx

∫

∫

0
1

π
2

206/I =

∫

0
ln 2

π
2

3

x3

7

203/I = ∫

v

oŸn h c !

2

x3
1− x2

dx

9

π
2 sin x.cos 3

2
2

x
230/I = ∫
dx
2
0 cos x + 1
1
2

0 x − 3x + 2
2

0

246/I =

dx

232*/I = ∫ x sin x.cos 2 xdx

247/I = ∫

0

π
2

0

2

cos x
dx
+
cos
2x
7
0
4
1
234/I = ∫ 2
dx
x
(x
+
1)
1
233/I = ∫

248/I =

7
π

x x +9

dx

dx

π
3

cos x + sin x
dx
3 + sin 2x
π

π
2
1

254*/I = ∫

4

−1

.

1 − sin x
dx
x
(1

+
cos
x)e
0

241/I = ∫

π
2

sin x
dx
2
0 cos x + 3

267/I = ∫

π
2

Xuct

x x2 −1

cos x
dx
0 7 + cos 2x
4
1
252/I = ∫

dx
2
1 (1 + x)x
2
x +1
253/I = ∫
dx
3
0 3x + 2

3
∫ cos x cos x − cos xdx

π2

3
∫ cos x cos x − cos xdx

−

dx

251/I = ∫

240*/I = ∫ ln( x 2 + a + x)dx

255/I =

4 − x2
1

π
2

0
π
2

π
2

x2

sin x
dx
1
sin
x
+
0

238/I = ∫ x sin 3 x cos 4 xdx

−

1− x2
dx
x2

250/I = ∫

236/I = ∫

2

dx

0
π
2

0
2

∫

1− x

2

249/I = ∫ x 5 (1 − x 3 )6 dx

235/I = ∫ sin 2x(1 + sin 2 x)3 dx

x +1
dx
3
0 3x + 2
4
1

∫

2
3
1

π
2

239/I =

∫

2
2
1

π

237/I =

∫

1

4x − 1

231/I = ∫

245/I =

x3

268/I =

π
2

om

∫

0

ang web chuy˚n n hi

v

oŸn h c !

sin x
dx
x

10


π
2

π
3

269/I = ∫ sin x cos x(1 + cos x) 2 dx

256/I = ∫ tg 4 xdx
π
4

π
2 1 + sin x

257*/I = ∫

0 1 + cos x

0
π
4

sin 4 x − cos 4 x
270/I = ∫
dx
+
+
sin
x
cos
x

1
0

e x dx

1

π
4

258/I = ∫ (1 − x 2 )3 dx

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

0
π
4

π
2

259/I = ∫ x.tg 2 xdx

sin x cos x + cos x
dx
sin
x
+
2
0

272/I = ∫

0
2

1
dx
2 2
(4
+
x
)
0
1
3x 2
261/I = ∫
dx
3
0 x +2

2
1 − x5
dx
262*/I = ∫
5
x(1
x
)
+
1
260/I= ∫

1

273/I = ∫

dx
3
x
a
1 3
x + 2x 2 + 10x + 1
274/I = ∫
dx
x 2 + 2x + 9
0
1
x3
275/I = ∫ 2
dx

3
(x
+
1)
0
1
3
276/I = ∫ 3
dx
x
+
1
0
1 4
x +1
277*/I = ∫ 6
dx
+
x
1
0
1
x
278/I = ∫
dx
3
0 (2x + 1)
7
1
279/I = ∫

dx
2 2 + x +1

π
3

cos x
dx
2
1
−
sin
x
0

263/I = ∫

π
3

sin 2 x
dx
6
0 cos x

264/I = ∫

π
6 sin x

+ sin 3 x
dx
cos 2x

265/I = ∫

0
π
2

1
dx
π sin x 1 + cos x

265/I = ∫

3
2

3
3

266/I =

1
ex

280/I =

1

∫

1
2

dx
∫ 6
2
1 x (1 + x )

2

295/I =

∫

2
3

om

ang web chuy˚n n hi

x 1− x

2

dx

.

.

Xuct

1

v

oŸn h c !

1
x x −1
2

dx
11


1

281*/I = ∫

x ln(x + 1 + x 2 )
1+ x

0

2

dx

4

297*/I = ∫
1

1
3

1

283/I = ∫ x 2 ln(x + 1) dx

298/I = ∫

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

286/I =

−1 (3 + 2x)
2
1

287/I = ∫

0
π
2

299/I =

x + 1+ x

2

dx

x + 1+ x2

dx

cos x
dx
0 cos x + 1

dx

π
2

cos x
dx
0 2 − cos x

302/I = ∫

π
2

sin x
dx
sin
x
2
+
0

303/I = ∫

π
2

4
π
2

cos3 x

304/I = ∫
dx
cos
x
1
+
0

290/I = ∫ (cos3 x + sin 3 x)dx

π
2

0
π
2

305/I =

291/I = ∫ cos5 x sin 4 xdx

1

∫ 2cos x + sin x + 3 dx

0

π
2

292/I = ∫ cos 2x(sin x + cos x)dx

π
3

π
4

1
293/I = ∫
dx
0 2 + sin x

ang web chuy˚n n hi

cos x

∫ (1 − cos x)2 dx

306/I =

4

0
π
2

om

dx

301/I = ∫

cos x + sin x
289/I = ∫
dx
3
+
sin
2x
π

Xuct

−1 1 +

2

6
π
2

π
2

4

+ 1+ x
1

dx

1
dx
4
sin
x
cos
x
π

cos x
288/I = ∫
dx
2
cos
2x
+
0

0
π
2

x 1+ x
x3

3

300/I = ∫

5 + 12x + 4x

1

∫

1+ x
1

dx

2

π
3

1

∫

3

0x
1

3

284/I = ∫

∫

0
2

282/I = ∫ (x − 1) 2 ln x dx

0
2

x3

7

296/I =

307/I = ∫ tg3 x dx
0

v

oŸn h c !

12


π
2

π

4

1
dx
0 2 − cos x

321*/I = ∫ tg5 x dx

294/I = ∫

0

π
4

1

1
dx
∫
2x
−1 3 + e
π
sin 2 x
dx
309*/I = ∫ x
+
3
1
−π

322/I = ∫ cotg 3 x dx

308*/I =

π
6
π
3

323/I =

π
2

π
4

sin x
dx
310*/I = ∫
cos
x
sin
x
+
0

π
4

π
2

sin 4 x
dx
4
4
+
cos
x
sin
x
0
tgx

312*/I = ∫

1 − ln 2 (cos x)

0

0

π
2

sin 5 x
dx
cos

x
1
+
0

325/I = ∫

dx

π
3

cos 2x
dx
2
π 1 − cos 2x

326/I = ∫

π
2

sin x
dx
+
cos
x
sin
x
0

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

1

315*/I = ∫ e
0
1

316*/I = ∫

0
π
2

3x +1

x

6

π
4

327*/I = ∫ (
0
1
1
2

2

dx

2 3

329*/I = ∫

cos x
dx
2
0 cos − 3cos x + 3
x
t 2et
318*/Tìm x> 0 sao cho ∫
dt = 1
2
(t
+
2)

0
317*/I = ∫

π
3

319*/I = ∫

π
4

1
ln 3

3

4

tan x
cos x cos 2 x + 1

330/I =

∫

0

x − x3
dx
x4

ex

(e + 1) e − 1

π
−1
e4

331/I =

t gx − 1 2
) dx
tgx + 1
x
dx
x3 + 1

328*/I = ∫

dx

x2 + 4

1

∫ 2 + tgx dx

324*/I =

311/I = ∫

π
2

4
∫ tg x dx

x

x

dx

1

dx
∫
2
1 x cos (ln x + 1)
e
π
4

dx

333*/I = ∫ ln(1 + tgx)dx
0

Xuct

om

ang web chuy˚n n hi

v

oŸn h c !

13


1

320*/I = ∫ −3x 2 + 6x + 1dx
0

.

Xuct

om

ang web chuy˚n n hi

v

oŸn h c !

14