cac bai toan ve tich phan luyen thi dai hoc 76700

Onthionline.net

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 để 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

12 / I =

2
4/I = ∫ 3tg x dx
π
4
π
4

π
2 3

π
6
π
2 1 − cos x

7/ I =

∫

4
∫ sin x dx
0

π
3

1
x
x dx
sin 2 cos 2
4
2
2

∫
π

15/I =

2

sin x.cos xdx

0

8/I =

π
3

∫

(2cos2 x-3sin2 x)dx

0

π
−x)
4
dx
9/ I= ∫
−πsin( π+x)
2
4
π
2

π
4

16/I =

∫π

−

sin(

π
2

2

x

sin 2x dx

π
4

2

18/

6

π
4
0

cotg2x dx

sin
17/I = ∫ e

(tgx-cotgx) dx

11/ I = cos 4 x dx
∫

∫

π
6

π
3

10 / I =

π
3

sin 3 x − sin x
cot gx dx
sin x

π
2

0

2

∫

13*/ I =

14/I =

∫ 1 + cos x dx

π
2

3
∫ sin x dx
0

2
5/I = ∫ (2cotg x + 5) dx

6/I =

π
2

.

I=

π
4

e tgx + 2
∫0 cos 2 x

Onthionline.net
1

34/I =

π
2

3

1
19/ I = ∫
dx
4
sin
x
π

35/I = ∫

2

π
4

1
∫0 cos 6 x dx

π

2

4

22/ I = cos xdx
∫

4sin 3 x
∫ 1 + cosx dx
0

1

0
1

5

1 + x 2 dx

0
1

x
dx
2x
+
1
0
1

1
dx
27/I = ∫ x
e
+
4
0
2
1
dx
28/I = ∫
−x
11− e
2
e 2x
dx
29/I = ∫ x
0 e +1
1
e− x
dx
30/I = ∫ − x
+1
0e
e
ln x
dx
31/I = ∫
2
x(ln

x
+
1)
1
26/I = ∫

32/I =

7
3

∫3

0

x +1
dx
3x + 1

dx

2

x x −9

dx

2
2
∫ x 4 − x dx

2
3
38/I = ∫ x (x + 4) dx
0

x2 − 4
dx
x

4

39/I =

∫

4 3
3
− 2

∫

40*/I =

−2
ln 2

41/I =

25/I = ∫ x

dx

−1
2

3
2
∫ x 1 − x dx

24/ I =

∫

2

2

2

3

0
π
2

23/ I =

4−x
1

x 16 − x
6
1
2 3

x + cos 4 x )dx

0

π
2

36*/I =
37/I =

∫ cos 2 x( sin

21/I =

x

2

4

4

20/ I =

1

∫

x2 +1

dx
x x +1
2

x
∫ e − 1dx

0
1

42/I = ∫

0
π
2

1
dx
3 − 2x

43/I = sin 5 xdx
∫
0

44*/I =

π
3

1

∫ cos x dx
0

e −2x
dx
45/I = ∫ − x
+1
0e
ln 3
1
dx
46/I = ∫
x
0
e +1
1

π
4

47/I = ∫

π

6

1
2

sin x cot gx

dx


Onthionline.net
2

3

2
33/I = ∫ (x − 3) x − 6x + 8 dx
0

.

ln x 3 2 + ln 2 x
48/I = ∫
dx
x
1
e

.

π
2

e

sin(ln x)
dx
x
1

64/I = sin x.sin 2x.sin 3xdx
∫

49/I = ∫

0
π
2

1

3
4
5
50/I = ∫ x (x − 1) dx

65/I = cos 2x(sin 4 x + cos 4 x)dx
∫

0

1

0

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

1

52/I = ∫

1+ x

1x
π
3

3

66*/I = ( 3 cos x − 3 sin x )dx
∫

dx

0

0

3
69/I = ∫ x. 1 − xdx

1

56/I =

∫

x

(e + 1)

0

3

1
2

x +1
dx
3
3x
+
2
0
π
6 x
dx

71*/I = ∫ sin
2
0
2
x
dx
72*/I = ∫
0 2+x + 2−x
70/I = ∫

dx

0

2x
3
57/I = ∫ x(e + x + 1)dx

58/I

−1
π
2
= 6

68*/I = 4cos x − 3sin x + 1 dx
9

0

1
dx
55*/I = ∫ 2x
e
+
3
0
ln 3
ex

π
2

∫ 4sin x + 3cos x + 5

(1 − x 2 )3 dx

54/I = ∫

x7
dx
67/I = ∫
8
4
2 1 + x − 2x
3

2
2
53/I = ∫ tg x + cot g x − 2dx

π
6
1

π
2

3

5

∫ 1 − cos x sin x.cos xdx

3

73/I =

0

0

2 3

59*/I =

∫

5

60/I =

π
4

2

x x +4

x
∫ 1 + cos 2x dx
0

ln 5

61/I =

1

∫

ln 2

e

2x

dx
e −1
x

3
2
∫ x . 1 + x dx

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

1

dx

74**/I = ∫
75/I =

π
2

sin x
∫ sin x + cos x dx
0

eπ

76/I = ∫ cos(ln x)dx
1

Onthionline.net

x2 +1
.ln xdx
62/I = ∫
x
1
e

2

1

x
dx
63/I = ∫
(x
+
1)
x
+
1
0

2

2
77*/I = ∫ 4 + x dx

0

2

x
dx
1 1 + x −1

78/I = ∫
.

1 + 3ln x ln x
dx
x

e

79/I = ∫

1
3

94/I =

2
80/I = ∫ ln(x − x)dx
2

cos x

∫ 6 − 5sin x + sin 2 x dx
0

e2

95*/I = ∫ (

e

e

2
81/I = ∫ (ln x) dx
e2

82/I = ∫
e

e2

83/I = ∫
1
2

1
1
−
)dx
ln 2 x ln x

3

96/I =

1

ln x
dx
x
ln x
dx
ln x

2
84/I = ∫ x ln(x + 1)dx
1
3

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

87/I =

π
6

2
∫ x − 4 dx

−4
2

3
2
97/I = ∫ x − 2x − x + 2 dx
−1
3π
4

98/I =

∫ cos 2x + 1dx

π
4
π

99/I = ∫ cos x

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 = ∫

2

cos x

π
6
2

dx

89/I = ∫ cos(ln x)dx
1

2

2
90*/I = ∫ ln( 1 + x − x)dx
0

∫ sin 2x dx

π
4
π
0
1

3

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

π

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


Onthionline.net
3

1

∫

91*/I =

2

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

dx

x4
dx
106*/I = ∫
x
1
+
2
−1
1

107/I =

108/I =

π2
4

∫ x cos xdx
0

π
6

1

109/I = x.sin x cos xdx
∫
2

0

x 2e x
dx
110*/I = ∫
2
(x
+
2)
0
1

π

111/I = ∫ e

2x

sin 2 xdx

0

2

1
x

2
112/I = ∫ x ln(1 + )dx
1
e

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

1
1
1
dx
125/I = ∫
2
2x
+
8x
+
26
−5
1
2x + 9
dx
126/I = ∫
0 x +3
4
1
dx
127/I = ∫ 2
1 x (x + 1)
123/I = ∫

ln x

dx
113/I = ∫ (x + 1) 2
1
e

1
2

114/I = x.ln 1 + x dx
∫
0

1− x

t

2

 ln x 
115/I = ∫ 
÷ dx ⇒ I < 2
x


1
π
3

116/I = sin x.ln(cos x)dx
∫

0

π
e2

2
∫ cos (ln x)dx

1
π
4

1

∫ cos x dx
0

sin 2x

∫ (2 + sin x) 2 dx
128*/I = −π
2

x −3
dx
2
(x
+
1)(x
+
3x
+
2)
0

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

129/I = ∫

0

118/I =

∫ x sin xdx
0

.

117/I =

π2
4

132/I =

π
3

sin 3 x
∫ (sin 2 x + 3) dx
0

π
3

4sin 3 x
dx
133/I = ∫
1
−
cos
x
π
6


Onthionline.net

119*/I =

π
4

π

3

1

1
dx
2
cos
x.sin
x
π

∫ cos3 x dx

134/I = ∫

0
1

6
π
3

3 x2

120/I = ∫ x e dx
0
π
2

135/I = sin x.tgxdx
∫

0
π
2

136/I =

0
π
3

121/I = esin 2 x .sin x cos3 xdx
∫
122/I =

sin 2x
∫ 1 + cos 4 x dx
0

sin 3 x
137/I =
∫ (tg 2 x + 1) 2 .cos5 x dx
0
138/I =

139/I =

140/I =

141/I =

1

1 + sin x

∫ 1 + 3cos x dx

143/I =

144/I =

∫

−3
π
3

∫

0
1

3

sin x
dx
cos x

145/I = ∫ x 1 − xdx
0

1+ e
1

2x

x 9+x

2

dx
dx

0
π
2

cos 4 x
∫ cos 4 x + sin 4 x dx
0

156/I = ∫

cos x

x + 4 + (x + 4)3

∫

1

0
π

∫ sin x + cos x + 1 dx
1
∫ x 2 (x + 1) dx
1
1
1

0
4

155/I =

3
dx
x+9 − x

157/I = ∫ x sin xdx

0
4

142/I =

∫

3e 4x + e 2x

154/I = e x sin 2 xdx
∫

cos x − 1

0
π
2

1
2

7
π
2

∫ cos x + 2 dx
π
−
2
π
2

152/I =

153/I =

∫ sin 2 x + 9cos 2 x dx
π
−
3
π
2

π
4

.

π
4

π
3

1

∫ sin 2x dx

0
π

2
2
158/I = ∫ x cos xdx

dx

0
1

159/I = ∫ cos x dx
0
1

160/I = ∫ sin x dx
0


Onthionline.net

x−4 1
.
dx
x+2 x+2
1
dx
2
x + 2x + 9
1
dx
2
4x − x

6

146/I = ∫

4
0

147/I =

∫

−1
3

148/I = ∫
1

2

2
∫ 4x − x + 5 dx

149/I =

−1
2

2x − 5

∫

150/I =

x 2 + 4x + 13
1
dx
x
3+e

−2
1

151/I = ∫

0
π

167/I = ∫ e

2x

dx

sin 2 x dx

0
1

x 2e x
dx
168/I = ∫
2
(x

+
2)
0
e

169/I = ∫ (1 + x) ln x dx
1
e

2
170/I = ∫ x ln x dx
1
1
e

171/I = ln 2 x dx
∫
1
e

172/I = ∫ x(2 − ln x) dx
1

e2

173/I = ∫ (
e
2

1

1
−
)dx
ln 2 x ln x

2
174/I = ∫ (x + x) ln x dx
1
2

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

161/I =

π2
4

∫ x sin x dx
0

2

162/I =

π
4

∫ x cos x dx

0
π

2
163/I = ∫ x cos x sin x dx

164/I =

0
π
6

2
∫ x cos x sin x dx

0
4

x

165/I = ∫ e

dx

1
π
4

166/I = e3x sin 4x dx
∫
182/I =

0
π
2

sin 2x

∫ 1 + cos 4 x dx

0
2

5
dx
x
−
6x
+
9
1
1 2
x + 3x + 2

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

1

2

15

1 + x 8 dx

188/I = ∫ x
0

ex

1

189/I = ∫

0

x

e +e

−x

dx


Onthionline.net
e

ln x
dx
∫
177/I = 1 (x + 1) 2
e

1
2

e

190/I=

∫ ln x dx

1
e
π
2

178/I = x ln 1 + x dx
∫

191/I = (esin x + cos x) cos x dx
∫

179/I = ∫ cos x.ln(1 − cos x) dx

192/I = sin 2x.cos x dx

1− x

0
π
2

0
π
2

∫ 1 + cos x
0

π
3

π
2

180/ esin
∫

π
2

2

x

sin x cos3 x dx

193/I = sin 2x + sin x dx

∫

0

181/I=

π
2

sin 2x
∫ 1 + sin 4 x dx
0

∫ 1 + sin 2x dx
0
3

∫

195/I =

.

2

197/I = ∫ (
−1
π
4

x −1 2
) dx
x+2

198/I = x.tg 2 x dx
∫
0
5

199/I = ∫ ( x + 2 − x − 2 )dx
−3
4

200/I = ∫

−1
2

201/I = ∫
1

2
dx
x+5 +4
x
dx
x+2 + 2−x

ln(1 + x)
dx
202/I = ∫
2
x

1
2

π
2

203/I = sin 2x dx
∫ 1 + cos x
0
204/I =

194/I =

1 + 3cos x
0
π
4 1 − 2sin 2 x

π
2

sin 2008 x
∫ sin 2008 x + cos 2008 x dx
0

0
π
3

196/I = ∫

π
4
1

x 5 + 2x 3
2

x +1

dx

tgx
2

cos x 1 + cos x

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

0 4−x
214/I =

215/I =

216/I =

1
2

x4
∫ 2 dx
0 x −1
π
2

sin 3x
∫ cos x + 1 dx
0
2
2

∫

x2
2

1− x
1− x2
dx

217/I = ∫
4
11+ x
0
2

dx

dx


Onthionline.net
π
2

205/I = sin x.ln(1 + cos x) dx
∫

218/I =

207/I =

3

∫

x2 +1
dx
x2

1
π
4 sin 3

x

∫ cos 2 x dx

0
π
2

208/I = cos 2 x.cos 4x dx
∫
0
1

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

e
1

1
dx
x +1 + x

211/I = ∫

0
π
2 1 + sin 2x

+ cos 2x
dx
cos x + sin x

227/I = ∫

π
6
1

x 2

(1 + e )
dx
2x
1

+
e
0

228/I = ∫

3

2
3
229/I = ∫ x (1 − x) dx

230/I =

231/I =

0
π
2

sin x.cos3 x
∫ cos 2 x + 1 dx
0

1
2

4x − 1

∫ x 2 − 3x + 2 dx

219/I =

3

2

dx

1+ x
1 − ex
dx
1 + ex

220/I = ∫ x 1 − x dx
0
1

2
221/I = ∫ x + 1dx
0
π
2

222/I = (cos3 x + sin 3 x) dx
∫
0
3

x2 +1

dx
223/I = ∫
0 x +1
1

2 2x
224/I = ∫ (1 + x) .e dx

225/I =

226/I =

0
π
2

∫

0
7
3

∫3

0

cos x
2

cos x + 1

dx

x +1
dx
3x + 1

.

π
2

242/I = sin 2x + sin x dx

∫

243/I =

244/I =

0
π
4

245/I =

cos3x + 1

sin 2x
∫ sin 2 x + 2cos 2 x dx

0
2
2

∫

0

π
0

∫

0
1

0

2
232*/I = ∫ x sin x.cos xdx

∫

0
ln 2

0

206/I =

x3

7

2
2

∫

0

x3
1− x

2

x3
1− x

2

dx

dx


Onthionline.net
π
2

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

∫

1

246/I =

0
2

x +1
dx
3

0 3x + 2
4
1

236/I = ∫
237/I =

∫

7

π

x x2 + 9

0
2

248/I =

dx
250/I =

0
π
2

π
2
1

2
240*/I = ∫ ln( x + a + x)dx

241/I =

π
2

2
3
1

−1

1 − sin x
∫ (1 + cos x)e x dx
0

0
π
2

π
−
2
π
3
π
4

x

∫ 1 + cos x e dx

2 3
258/I = ∫ (1 − x ) dx
0

sin x

0
π
2

∫

cos x + sin x
dx
3 + sin 2x
π

254*/I = ∫

.

268/I =

0
1

x x −1

dx

π
3

267/I =

4
256/I = ∫ tg xdx

257*/I =

2

4

3
∫ cos x cos x − cos xdx

π
2 1 + sin x

dx

∫ 1 + sin x dx

π

2

255/I =

4−x
1

2

cos x
dx
7
+
cos
2x
0
4
1
dx
252/I = ∫
2
1 (1 + x)x
2
x +1
dx
253/I = ∫ 3
0 3x + 2
251/I =

3

∫ cos x cos x − cos xdx

−

∫

x2

5
3 6
249/I = ∫ x (1 − x ) dx

3
4
238/I = ∫ x sin x cos xdx

239/I =

2
2
1

247/I = ∫

π
2

235/I = sin 2x(1 + sin 2 x)3 dx
∫

∫

1− x2
dx
x2

π
2

sin x
∫ cos 2 x + 3 dx
0

π2

∫

0
π
2

sin x
dx
x

269/I = sin x cos x(1 + cos x) 2 dx
∫
0

Onthionline.net
π
4

π
4

4
4
270/I = sin x − cos x dx
∫

259/I = x.tg 2 xdx
∫
0
2

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

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

263/I =

π
3

π
4

4
4
271/I = sin x − cos x dx
∫

272/I = sin x cos x + cos x dx

∫

273/I =

∫ cos6 x

0
π
6

3
265/I = sin x + sin x dx

cos 2x

1
dx
sin
x
1
+
cos
x
π

265/I = ∫

3

1

∫ x 6 (1 + x 2 ) dx

1

.

1

281*/I = ∫

2

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

0

4

2

2
282/I = ∫ (x − 1) ln x dx
1
3

2

283/I = ∫ x ln(x + 1) dx

dx

280/I =

∫ x 3 dx

3
2

∫

1
2

1
x 1− x

2

dx

.

295/I =

0
2

3x 3
dx
284/I = ∫ 2
x

+
2x
+
1
1

1
ex

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

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

2

264/I = sin x dx

266/I =

1
a
1

0
π
3

3

sin x + 2

0

cos x

0
π
2

sin x + cos x + 1

0
π
2

∫ 1 − sin 2 x dx

∫

sin x + cos x + 1

0

2

1

2
3

2

∫

x x −1
x3

7

296/I =

∫

0

3

1+ x

2

dx

dx


Onthionline.net

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

1
2

286/I =

288/I =

1

∫

5 + 12x + 4x 2

1

x + 1+ x

0
π
2

297*/I = ∫
1

1

−1 (3 + 2x)
2
1

287/I = ∫

2

dx

dx

cos x
dx
2 + cos 2x

∫

0
π
2

cos x + sin x
dx
3 + sin 2x
π

289/I = ∫

4
π
2

298/I = ∫

299/I = ∫

301/I =

292/I = cos 2x(sin 4 x + cos 4 x)dx
∫

304/I =

294/I =

1
∫ 2 + sin x dx
0

1

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

310*/I =

π
2

sin x

∫ cos x + sin x dx
0

dx

x + 1+ x

2

dx

305/I =

4

6
π
2

cos x

∫ cos x + 1 dx

0
π
2

cos x

∫ 2 − cos x dx

0
π
2

sin x

∫ sin x + 2 dx

0
π
2

cos3 x
∫ cos x + 1 dx
0
π
2

1

∫ 2cos x + sin x + 3 dx
0

π
2

1
∫ 2 − cos x dx
0

2

1
dx
sin
x
cos
x
π

300/I = ∫

303/I =

293/I =

dx

π
3

291/I = cos5 x sin 4 xdx
∫

0
π

2

3

+ 1+ x
1

−1 1 +

302/I =

0
π
2

x 1+ x
x3

0x
1

290/I = (cos3 x + sin 3 x)dx
∫
0
π
2

1

π

2

cos x

∫ (1 − cos x)2 dx

306/I =

π
3
π
4

307/I = tg 3 x dx
∫
0

π
4

321*/I = tg 5 x dx
∫
0


Onthionline.net

311/I =

π

2

π
4

4

sin x

3
322/I = ∫ cotg x dx

∫ cos 4 x + sin 4 x dx

π
6
π
3

0

π
2

tgx

312*/I = ∫

2

1 − ln (cos x)

0

dx

323/I =

π
2

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

∫

1

315*/I = ∫ e
0
1

316*/I = ∫

0
π
2

3x +1

x

π
3

319*/I = ∫

325/I =

π
4
1

π
2

sin 5 x

∫ cos x + 1 dx
0

cos 2x
dx
2
π 1 − cos 2x

dx

326/I = ∫

6

3

cos x cos 2 x + 1

1

∫ 2 + tgx dx

π
3

2

tan x

π

4
0

π
4

cos x
∫ cos 4 − 3cos 2 x + 3 dx
0
x
t 2et
dt = 1
318*/Tìm x> 0 sao cho ∫
2
(t
+
2)
0
317*/I =

π
4

324*/I =

dx

x2 + 4

4

∫ tg x dx

327*/I = ( t gx − 1) 2 dx
∫

tgx + 1

0
1

x

328*/I = ∫ x 3 + 1dx
1
2

dx

2 3

329*/I = ∫

1
ln 3

2

320*/I = ∫ −3x + 6x + 1dx

330/I =

0

∫

0

∫

1
e
π
4

x

x

(e + 1) e − 1

π
−1
e4

331/I =

x − x3
dx
x4
ex

1
dx
x cos 2 (ln x + 1)

333*/I = ln(1 + tgx)dx
∫
0

.

dx


Onthionline.net