255 bài toán tích phân luyện thi đại học

 1 
255 BÀI TOÁN TÍCH PHÂN 
 LUYỆN THI ĐẠI HỌC 
 BIÊN SOẠN: NGUYỄN ĐỨC BÁ GV THPT TIỂU LA TB-QUẢNG NAM-TEL : 0985 378 214 
TÍNH : 
1/I = 
2
0
1 cos x
dx
1 cos x



 
 2/ I = 
4
4
0
cos x dx

 
3/ I = 
2
4
4sin
1

 x dx 
4/ I = 
4
0
6cos
1

x
 dx 
5/I= dxxxnsix )cos(2cos
44
2
0


6/ I = 
32
0
4sin x
dx
1 cosx


 
7/ I =
1
2
0
3x 6x 1dx   
8/I =
1
5 2
0
x 1 x dx 
9/I =
1
0
x
dx
2x 1
 
10/I =
1
x
0
1
dx
e 4
 
11/I =
2
x
1
1
dx
1 e
 
12/I =
2x2
x
0
e
dx
e 1
 
13/I =
x1
x
0
e
dx
e 1

 
 
14 /*I =
3 32
4
1
x x
dx
x

 
15/I =
3
2
4
tan x
dx
cos x cos x 1

 
 
16/I = 
1
4e
2
1
e
1
dx
x cos (ln x 1)



 
 17/ I = 
xln 3
x x
0
e
dx
(e 1) e 1 
 
18/I =
1
2 2
3
1
dx
x 4 x
 
19/I =
4
2
2
1
dx
x 16 x
 
20*/I =
6
2
2 3
1
dx
x x 9
 
21/I =
2
2 2
1
x 4 x dx

 
22/I =
2
2 3
0
x (x 4) dx 
23/I =
24
4 3
3
x 4
dx
x

 
24*/I =
22
2
2
x 1
dx
x x 1




 
25/I =
ln 2
x
0
e 1dx 
26/I =
2
5
0
sin xdx

 
 2 
27/I =
e
2
1
ln x
dx
x(ln x 1)
 
28/I =
7
3
3
0
x 1
dx
3x 1


 
29/I =
2
3 2
0
(x 3) x 6x 8 dx   
30/I =
2
3
1
dx
sin x 1 cos x

 
 
31/I =
1
3 4 5
0
x (x 1) dx 
32/I =
1
2 3
0
(1 2x)(1 3x 3x ) dx   
33/I =
2
3
1
1
dx
x 1 x
 
34/I =
1
2 3
0
(1 x ) dx 
35*/I =
1
2x
0
1
dx
e 3
 
36/I =
xln 3
x 3
0
e
dx
(e 1)
 
37/I =
0
2x 3
1
x(e x 1)dx

  
38/I =
2
6 3 5
0
1 cos x sin x.cos xdx

 
39*/I =
2 3
2
5
1
dx
x x 4
 
40/I =
4
0
x
dx
1 cos 2x


 
41/I =
2xln 5
x
ln 2
e
dx
e 1
 
42*/I =
3
0
1
dx
cos x

 
43/I =
2x1
x
0
e
dx
e 1

 
 
44/I =
ln 3
x
0
1
dx
e 1
 
45/I =
4
2
6
1
dx
sin x cot x


 
46/I =
3 2e
1
ln x 2 ln x
dx
x

 
GV: NGUYỄN ĐỨC BÁ-THPT TIỂU LA THĂNG BÌNH 
47/I =
2
0
sin x.sin 2x.sin 3xdx

 
48/I =
73
8 4
2
x
dx
1 x 2x 
 
49*/I =
2
0
4cos x 3sin x 1
dx
4sin x 3cos x 5

 
 
 
50/I =
9
3
1
x. 1 xdx 
51*/I =
6
0
x
sin dx
2

 
52*/I =
2
0
x
dx
2 x 2 x  
 
53**/I =
1
2
0
ln(1 x)
dx
x 1


 
54/I =
2
0
sin x
dx
sin x cos x


 
55/I =
e
1
cos(ln x)dx

 
 3 
56*/I =
2
2
0
4 x dx 
57/I =
2e
1
x 1
.ln xdx
x

 
58/I =
21
0
x
dx
(x 1) x 1 
 
59/I =
2
3 2
0
(cos x 1)cos x dx

 
60/I =
3
2
2
ln(x x)dx 
61/I =
2e
e
ln x
dx
x
 
62/I =
2e
1
ln x
dx
ln x
 
63/I =
1
3
1
2
x
dx
x 1
 
64/I =
3
2
3
1
dx
x 3
 
65/I =
3
2
6
ln(sin x)
dx
cos x


 
66/I =
3
4
4
cos2x 1dx


 
67*/I =
2
2
0
ln( 1 x x)dx  
68*/I =
3
2
2
1
dx
x 1
 
GV: NGUYỄN ĐỨC BÁ-THPT TIỂU LA THĂNG BÌNH 
69/I =
38
1
x 1
dx
x

 
70/I =
33
2
1
x
dx
x 16
 
71/I =
6
2
0
x.sin x cos xdx

 
72/I =
2
1
x
dx
1 x 1 
 
GV: NGUYỄN ĐỨC BÁ-THPT TIỂU LA THĂNG BÌNH 
73/I =
6
2
0
cos x
dx
6 5sin x sin x

 
 
74*/I =
2e
2
e
1 1
( )dx
ln xln x
 
75/I =
0
cos x sin xdx

 
76/I =
2
0
1 sin xdx

 
77/I =
3
4
4
sin 2x dx


 
78/I =
0
1 sin xdx

 
79/I =
1 3
2
1
ln(x x 1) dx

    
80*/I =
2
0
x sin x
dx
1 cos x


 
81*/I =
1
2 x
1
1
dx
(x 1)(4 1)  
 
82*/I =
41
x
1
x
dx
1 2 
 
83/I =
2
4
0
x sin xdx

 
 4 
84/I =
2
4
0
x cos xdx

 
85/I =
6
2
0
x.sin x cos xdx

 
86*/I =
2 x1
2
0
x e
dx
(x 2)
 
87/I =
2x 2
0
e sin xdx

 
88/I =
2
2
1
1
x ln(1 )dx
x
 
89/I =
e
2
1
e
ln x
dx
(x 1)
 
90/I =
1
2
0
1 x
x.ln dx
1 x


 
91/I =
2t
1
ln x
dx I 2
x
 
  
 
 
92/I =
3
0
sin x.ln(cos x)dx

 
93/I =
2e
2
1
cos (ln x)dx

 
94*/I =
4
3
0
1
dx
cos x

 
95/I =
2
1
3 x
0
x e dx 
96/I =
22 sin x 3
0
e .sin x cos xdx

 
97/I =
2
4
0
sin 2x
dx
1 cos x


 
98/I = 
34
2 2 5
0
sin x
dx
(tan x 1) .cos x


 
99/I =
1
2
5
1
dx
2x 8x 26  
 
100/I =
4
2
1
1
dx
x (x 1)
 
101*/I =
0
2
2
sin 2x
dx
(2 sin x) 
 
102/I =
1
2
0
x 3
dx
(x 1)(x 3x 2)

  
 
103/I =
1
3
0
4x
dx
x 1
 
104/I =
1
4 2
0
1
dx
x 4x 3 
 
105/I =
33
2
0
sin x
dx
sin x 3


 
106/I =
xln 3
x x
0
e
dx
(e 1) e 1 
 
107/I =
3
2
6
1
dx
cos x.sin x


 
108/I =
3
2 2
3
1
dx
sin x 9cos x




 
109/I = 
3
4
1
dx
sin 2x


 
GV: NGUYỄN ĐỨC BÁ-THPT TIỂU LA THĂNG BÌNH 
110/I = 
1
4x 2x2
2x
0
3e e
dx
1 e


 
 5 
111/I = 
2
x 2
0
e sin xdx

 
112/I = 
42
4 4
0
cos x
dx
cos x sin x


 
113/I =
1
0
3
dx
x 9 x 
 
114/I = 
2
0
1 sin x
dx
1 3cos x



 
115/I =
2
0
cos x
dx
sin x cos x 1

 
 
116/I =
1
3
3
1
dx
x 4 (x 4)   
 
117/I =
1
0
x 1 xdx 
118/I =
6
4
x 4 1
. dx
x 2 x 2

 
 
119/I = 
0
2
1
1
dx
x 2x 9  
 
120/I =
3
2
1
1
dx
4x x
 
121/I = 
2
2
1
4x x 5 dx

  
122/I = 
2
2
2
2x 5
dx
x 4x 13

 
 
123/I =
1
x
0
1
dx
3 e
 
124/I =
2x 2
0
e sin x dx

 
125/I =
2 x1
2
0
x e
dx
(x 2)
 
126/I =
e
1
x(2 ln x)dx 
127/I =
5 33
2
0
x 2x
dx
x 1


 
128/I =
2
2
1
(x x) ln x dx 
129/I =
2
2
1
1
x ln(1 )dx
x
 
130/I =
4
3x
0
e sin 4x dx

 
131/I =
2
4
0
sin 2x
dx
1 cos x


 
132/I =
21
0
x 3x 2
dx
x 3
 

 
133/I =
1
2
0
ln(1 x)
dx
x 1


 
134/I
41
6
0
1 x
dx
1 x


 
135/I =
1
15 8
0
x 1 x dx 
136/I =
x1
x x
0
e
dx
e e
 
137/I= 
e
1
e
ln x dx 
138/I =
2
5
1
ln x
dx
x
 
139/I =
2
0
sin 2x.cos x
dx
1 cos x


 
140/I =
2
0
sin 2x sin x
dx
1 3cos x



 
 6 
141/I =
24
0
1 2sin x
dx
1 sin 2x



 
142/I =
2
2
1
(x x) ln x dx 
143/I =
21
2
0
x
dx
4 x
 
144/I =
1
42
2
0
x
dx
x 1
 
145/I =
e
2
1
e
ln x
dx
(x 1)
 
146/I =
1
2
0
1 x
x ln dx
1 x


 
147/I =
2
3
cos x.ln(1 cos x)dx


 
148/
22 sin x 3
0
e sin x cos x dx

 
149/I= 
2
4
0
sin 2x
dx
1 sin x


 
GV: NGUYỄN ĐỨC BÁ-THPT TIỂU LA THĂNG BÌNH 
150/I =
2
2
1
x 1
( ) dx
x 2


 
151/I =
4
2
0
x.tan x dx

 
152/I =
5
3
( x 2 x 2 )dx

   
153/I =
4
1
2
dx
x 5 4  
 
154/I =
2
1
x
dx
x 2 2 x  
 
155/I =
2
2
1
ln(1 x)
dx
x

 
156/I =
2
0
sin 2x
dx
1 cos x


 
157/I =
20102
2010 2010
0
sin x
dx
sin x cos x


 
158/I =
2
0
sin x.ln(1 cos x)dx

 
159/I =
3
4
4
tan x dx


 
160/I =
4
5
0
tan x dx

 
161/I =
22
4
1
1 x
dx
1 x


 
162/I =
37
3 2
0
x
dx
1 x
 
163/I =
xln 2
x
0
1 e
dx
1 e


 
164/I =
52
0
sin x
dx
cos x 1


 
165/I =
4
2
0
tan x 1
( ) dx
tan x 1



 
166/I =
23
0
x 1
dx
x 1


 
167/I =
1
2 2x
0
(1 x) .e dx 
 7 
168/I =
2
2
0
cos x
dx
cos x 1


 
169/I =
7
3
3
0
x 1
dx
3x 1


 
GV: NGUYỄN ĐỨC BÁ-THPT TIỂU LA THĂNG BÌNH 
170/I =
2
0
sin 2x sin x
dx
cos3x 1



 
171/I =
4
2 2
0
sin 2x
dx
sin x 2cos x


 
172/I =
2
32
2
0
x
dx
1 x
 
173/I =
23
2
1
x 1
dx
x

 
174/I =
34
2
0
sin x
dx
cos x

 
175/I =
2
2
0
cos x.cos4x dx

 
176/I =
1
2x x
0
1
dx
e e
 
177/I =
1
0
1
dx
x 1 x 
 
178/I =
2
6
1 sin 2x cos 2x
dx
cos x sin x


 

 
179/I =
x 21
2x
0
(1 e )
dx
1 e


 
180/I =
2
2
3
cos x
dx
(1 cos x)

 
 
181/I = 
32
2
0
sin x.cos x
dx
cos x 1


 
182/I =
1
2
2
0
4x 1
dx
x 3x 2

 
 
183/I =
2
0
cos x
dx
cos 2x 7


 
184/I =
2
2 3
0
sin 2x(1 sin x) dx

 
185/I =
2
3
0
x 1
dx
3x 2


 
186/I =
4
2
7
1
dx
x x 9
 
187/I =
2
0
cos x
dx
2 cos x


 
188/I =
2
2
2
3
1
dx
x x 1
 
189/I =
1
5 3 6
0
x (1 x ) dx 
190/I =
2
0
sin x
dx
1 sin x


 
191/I =
2
0
cos x
dx
7 cos2x


 
192/I =
4
2
1
1
dx
(1 x)x
 
 8 
193*/I =
3
4
cos x sin x
dx
3 sin 2x




 
194/I =
2
2
0
sin x
dx
cos x 3


 
195/I=
2
2
0
sin x
dx
cos x 3


 
196/I =
2
0
sin x
dx
x

 
197/I =
2
2
0
sin x cos x(1 cos x) dx

 
198/I =
4 44
0
sin x cos x
dx
sin x cos x 1


 
 
199/I =
2
0
sin x cos x cos x
dx
sin x 2



 
200/I =
3 4
0
x sin x cos xdx

 
201/I =
2
3
2
cos x cos x cos xdx



 
202*/I =
2
x
0
1 sin x
e dx
1 cos x



 
203/I =
1
2 3
0
(1 x ) dx 
204/I=
2
2 2
0
1
dx
(4 x )
 
205/I = 
21
3
0
3x
dx
x 2
 
206*/I = 
52
5
1
1 x
dx
x(1 x )


 
207/I =
3
2
0
cos x
dx
1 sin x


 
208/I =
23
6
0
sin x
dx
cos x

 
209/I =
36
0
sin x sin x
dx
cos 2x


 
210/I =
2
3
1
dx
sin x 1 cos x

 
 
211/I =
3
6 2
1
1
dx
x (1 x )
 
212*I =
21
2
0
x ln(x 1 x )
dx
1 x
 

 
213/I =
4
2
1
(x 1) ln x dx 
214/I =
32
2
1
3x
dx
x 2x 1 
 
215/I =
1
1 x
3
a
e
dx
x
 
216/I =
3 21
2
0
x 2x 10x 1
dx
x 2x 9
  
 
 
217/I =
31
2 3
0
x
dx
(x 1)
 
218/I =
1
3
0
3
dx
x 1
 
219*/I =
41
6
0
x 1
dx
x 1


 
220/I =
1
3
0
x
dx
(2x 1)
 
221/I =
7
2
1
dx
2 x 1 
 
 9 
222/I =
42
4 4
0
cos x
dx
cos x sin x


 
223/I =
33
0
sin x
dx
cos x

 
224/I =
37
3 2
0
x
dx
1 x
 
225*/I =
2
3
1
1
dx
x 1 x
 
226/I =
31
2
0
x
dx
x 1 x 
 
227/I =
1
2
1
1
dx
1 x 1 x   
 
228/I =
3
4
6
1
dx
sin x cos x


 
229/I =
4
3
6
cot x dx


 
230/I =
1
3 2
0
4x 1
dx
x 2x x 2

  
 
231/I = 
1
2
21
2
1
dx
(3 2x) 5 12x 4x   
 
232/I =
1
0
1
dx
x 1 x 
 
233/I =
2
0
cos x
dx
2 cos 2x


 
234/I =
2
4
cos x sin x
dx
3 sin 2x




 
235/I =
2
3 3
0
(cos x sin x)dx

 
236/I =
2
5 4
0
cos x sin xdx

 
237/I =
4
x
1
e dx 
238*/I =
1
x 2
1
1
dx
(e 1)(x 1)  
 
239*/I =
32
4 2
0
cos x
dx
cos 3cos x 3

 
 
240*/Tìm x> 0 sao cho 
2 tx
2
0
t e
dt 1
(t 2)


 
241/I =
xln 3
x x
0
e
dx
(e 1) e 1 
 
 242/I =
2
2
cos x 1
dx
cos x 2





 
243/I =
2
0
sin x
dx
sin x 2


 
244/I =
3
2
1
3 ln x
dx
(x 1)


 
245/I = 
2
0
1
dx
2cos x sin x 3

 
 
246/I =
2
0
1
dx
2 sin x


 
247/I =
2
0
1
dx
2 cos x


 
248*/I =
1
2x
1
1
dx
3 e 
 
 10 
249*/I =
2
x
sin x
dx
3 1

 
 
250*/I =
2
2
0
tan x
dx
1 ln (cos x)


 
251*/I =
2
0
sin x
dx
cos x sin x


 
252*/I =
1
3x 1
0
e dx 
253*/I =
21
2
0
x
dx
x 4
 
254*/I =
43
2
0
x 1
dx
x 9


 
255*/I =
23
4
1
x 1
dx
x 1


 235/I 
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