1. 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 
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 :

3

2
4/I =  3tg 2 x dx

4

4
5/I =
6/I =
3
 sin x dx
12 / I =
0

2 3

6

2 1  cos x

0 1  cos x

3

2
dx
4
 sin x dx
14/I =
0


2
3
1
x
x dx
sin 2 cos 2
4
2
2


15/I =
7/ I =  sin2 x.cos2xdx
0

3
8/I =

(2cos2 x-3sin2 x)dx
0
9/ I=

2


2

 x)
4
dx

sin(  x)
4

4
16/I =
sin(


17/I =
cotg2x dx
e
sin 2 x
sin 2x dx

4

4
(tgx-cotgx)2 dx
18/
6

4
11/ I =  cos 4 x dx


6

2

3
10 / I =

13*/ I =
2
 (2cotg x  5) dx
sin 3 x  sin x
cot gx dx
sin x
e tgx 2
2
I= 
0 cos x
.
0
1
34/I =

3
1
x
2
4x
2
dx

2. 
4
35/I = 
2
1
19/ I =  sin 4 x dx

2
36*/I =
4

1
 cos
6
0
x
dx
2
4
4
 cos 2 x(sin x  cos x)dx
37/I =
0
4sin 3 x
23/ I = 
dx
1  cosx
0
1
 x 1  x dx
24/ I =
3
25/I =  x
5
2
1  x dx
2
x
dx
2x  1
0
1
1
27/I =  x
dx
e 4
0
2
1
dx
28/I = 
x
1 1 e
2
e2x
dx
29/I =  x
0 e 1
1
e x
dx
30/I =   x
1
0e
e
ln x
dx
31/I = 
x(ln 2 x  1)
1
26/I = 
32/I = 
0
2
x 1
dx
3
3x  1
33/I =  (x  3) x 2  6x  8 dx
0
.
3

40*/I =
2
ln 2
41/I =
x2 1
dx
x x 1
2
x
 e  1dx
0
1
42/I = 
0

2
0
1
7
3

 2
0
1
x2  4
dx
x
4 3
3
0

2
dx
38/I =  x (x 2  4)3 dx
39/I =
22/ I =  cos xdx
x x 9
2
2
2
 x 4  x dx
4
3
dx
1
2
0

2

2
2

21/I =
x 16  x
6
1
2 3
4
20/ I =
1
1
dx
3  2x
43/I =  sin 5 xdx
0

3
1
dx
cos x
0
44*/I = 
e2x
45/I =   x
dx
e 1
0
ln 3
1
dx
46/I = 
x
0
e 1
1

4
47/I = 

6
1
2
sin x cot gx
dx
ln x 3 2  ln 2 x
dx
48/I = 
x
1
e
.

3. 
2
e
sin(ln x)
dx
x
1
64/I =  sin x.sin 2x.sin 3xdx
49/I = 
0

2
1
50/I =  x 3 (x 4  1)5 dx
0
1
65/I =  cos 2x(sin 4 x  cos 4 x)dx
0
51/I =  (1  2x)(1  3x  3x ) dx

2
2 3
0
2
66*/I =  ( 3 cos x  3 sin x )dx
1
52/I = 
1 x
1x

3
3
0
dx
x7
67/I = 
dx
1  x 8  2x 4
2
3
53/I =  tg 2 x  cot g 2 x  2dx

6
1
4cos x  3sin x  1
dx
4sin x  3cos x  5
0
68*/I = 
54/I =  (1  x 2 )3 dx
9
69/I =  x. 3 1  xdx
0
1
2
1
1
55*/I =  2x
dx
e 3
0
ln 3
ex
56/I =

2

(e  1)
x
0
3
x 1
dx
3
0 3x  2

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

2
6
3
58/I =  1  cos x sin x.cos xdx
3
5
73/I =
0
0
59*/I =

5
1
x x 4
2
dx

4
x
dx
60/I = 
1  cos 2x
0
ln 5

e
2x
dx
x
ln 2 e  1
e 2
x 1
.ln xdx
62/I = 
x
1
1
ln(1  x)
dx
x2 1
0
1
2 3
61/I =
3
2
 x . 1  x dx
2
x
dx
63/I = 
(x  1) x  1
0
74**/I = 

2
sin x
dx
sin x  cos x
0
75/I = 
e
76/I =  cos(ln x)dx
1
2
77*/I =  4  x 2 dx
0
2
x
dx
1 1  x 1
78/I = 
.

4. 1  3ln x ln x
dx
x
e
79/I = 
1
3
80/I =  ln(x 2  x)dx
2

6
cos x
dx
6  5sin x  sin 2 x
0
94/I = 
e2
95*/I =  (
e
3
e
81/I =  (ln x) dx
2
96/I =
e
2
ln x
dx
x
97/I =
ln x
dx
ln x
98/I =

e
e2
83/I =

1
2
85/I =
1
1
0
4x
86/I = 
2
 cos 2x  1dx

4

99/I =  cos x
sin xdx
0
 x 2  3 dx
3
1
3
2
 x  2x  x  2 dx
1
3
4
84/I =  x ln(x 2  1)dx
1
3
2
 x  4 dx
4
2
1
82/I =
1
1

)dx
ln 2 x ln x
2
100/I =
 1  sin xdx
0
3
4
dx
 sin 2x dx

4
101/I =
0

3 ln(sin x)
102/I =  1  sin xdx
2
87/I =

4

 sin xdx
88/I = 
2
cos x

6
2
dx
1
2
90*/I =  ln( 1  x 2  x)dx
0
3

1
x 1
x 1
dx
92/I = 
x
1
3
x3
dx
93/I =  2
x  16
1
2
3
8
2
dx
x sin x
dx
1  cos 2 x
0
1
1
dx
105*/I =  2
x
1 (x  1)(4  1)
1
x4
dx
106*/I = 
x
1 1  2
104*/I = 
2
4
107/I =
 x sin xdx
0
2
4
108/I =
.
3
103/I =  ln(x  x 2  1)  dx




1

89/I =  cos(ln x)dx
91*/I =
0
1
 x cos xdx
0

5. 
6
1
109/I =  x.sin x cos xdx
2
0
x 2ex
110*/I = 
dx
(x  2) 2
0
1

111/I =  e2x sin 2 xdx
0
2
1
x
112/I =  x 2 ln(1  )dx
1
3
dx
x  4x  5
0
2
5
124/I =  2
dx
1 x  6x  9
1
1
125/I = 
dx
2x 2  8x  26
5
1
2x  9
126/I = 
dx
x 3
0
4
1
127/I =  2
dx
x (x  1)
1
123/I = 
2
e
ln x
dx
2
1 (x  1)
113/I = 
e
1
2
0
128*/I =
2
114/I =  x.ln
0
1 x
dx
1 x
129/I = 
2

3
116/I =  sin x.ln(cos x)dx
0

3
sin 3 x
dx
132/I = 
(sin 2 x  3)
0

e2
2
 cos (ln x)dx

3
1

4
4sin 3 x
dx
133/I = 
 1  cos x
1
dx
cos x
0
118/I = 
6

3

4
1
dx
cos x.sin 2 x

1
dx
cos3 x
0
134/I = 
119*/I = 
1
x 3
dx
(x  1)(x 2  3x  2)
0
1
4x
130/I =  3
dx
(x  1)
0
1
1
131/I =  4
dx
(x  4x 2  3)
0
1
 ln x 
115/I =  
 dx  I  2
 x 
1
t
117/I =
6

3
3 x2
120/I =  x e dx
0

2
121/I =  e
0

2
sin 2x
dx

2
 (2  sin x)
135/I =  sin x.tgxdx
sin 2 x
0

3
3
.sin x cos xdx
sin 2x
dx
122/I = 
4
0 1  cos x
136/I =

4
.
1
 sin 2x dx

6. 
4
sin x
137/I = 
dx
(tg 2 x  1) 2 .cos5 x
0

3
138/I =
1
2
3
152/I =
139/I =
140/I =
154/I =
cos x  1
1  sin x
 1  3cos x dx
3
156/I = 
x  4  (x  4)

3
sin 3 x
144/I = 
dx
cos x
0
0

0

158/I =  x 2 cos 2 xdx
3
dx
0
1
159/I =  cos x dx
0
1
160/I =  sin x dx
0
2
4
145/I =  x 1  xdx
x4 1
.
dx
146/I = 
x2 x2
4
0
1
dx
147/I = 
2
1 x  2x  9
3
1
dx
148/I = 
2
1 4x  x
 4x  x  5 dx
1
2
150/I =

2
2x  5
x 2  4x  13
1
dx
151/I = 
x
0 3 e
2
1
 x sin x dx
161/I =
0
6
149/I =
3
dx
x 9  x
157/I =  x sin xdx
1
2
dx
x
2
 e sin xdx
1
cos x
141/I = 
dx
sin x  cos x  1
0
4
1
142/I =  2
dx
x (x  1)
1
1
1

x 9x
2
dx
cos 4 x
155/I = 
dx
cos 4 x  sin 4 x
0
0

2
143/I =
2x
0

2
 cos x  2 dx


2

2

7

2

3

2
1 e
1
0
4
153/I =
1
 sin 2 x  9cos 2 x dx


3e4x  e2x
dx
0

4
2
162/I =
 x cos x dx
0

163/I =  x cos 2 x sin x dx
0

6
164/I =
2
 x cos x sin x dx
0
4
165/I =  e
1

4
x
dx
166/I =  e3x sin 4x dx
0

7. 
167/I =  e
2x
2
sin x dx
0
1
x 2ex
168/I = 
dx
(x  2) 2
0
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
e2
1
1
)dx
173/I =  ( 2 
ln x
e ln x

2
sin 2x
dx
1  cos 4 x
0
2
5
183/I =  2
dx
x  6x  9
1
1 2
x  3x  2
184/I = 
dx
x 3
0
4
1
185/I =  2
dx
1 x (x  1)
1
ln(1  x)
186/I =  2
dx
x 1
0
1
1 x4
187/I 
dx
1  x6
0
182/I = 
1
188/I =  x15 1  x 8 dx
0
2
174/I =  (x 2  x) ln x dx
1
2
1
x
175/I =  x 2 ln(1  ) dx
1
2
ln x
176/I =  5 dx
1 x
e
ln x
dx
177/I = 
2
1 (x  1)
e
1
2
178/I =  x ln
0

2
1 x
dx
1 x
189/I = 
190/I=
1
e

2
191/I =  (esin x  cos x) cos x dx
0

2
sin 2x.cos x
dx
1  cos x
0
192/I = 

2
sin 2x  sin x
dx
1  3cos x
0
2
x
sin x cos3 x dx
x
dx
1  sin 2x
3

195/I =
0
sin 2x
 1  sin 4 x dx
0
.

4 1  2sin 2
194/I = 
0

2
dx
 ln x dx
0
180/  esin
x
193/I = 

3
181/I=
e e
x
0
e
179/I =  cos x.ln(1  cos x) dx

2
ex
1

3
196/I = 

4
x 5  2x 3
x 1
2
dx
tgx
cos x 1  cos x
2
dx

8. x 1 2
197/I =  (
) dx
x2
1
2

4
198/I =  x.tg 2 x dx
0
5
199/I =
 ( x  2  x  2 ) dx
3
4
2
dx

1 x  5  4
2
x
201/I = 
dx
x 2  2x
1
200/I =
x2
212/I = 
dx
4  x2
0
1
x
213/I = 
dx
4  x2
0
1
1
2
x4
214/I =  2
dx
x 1
0

2
sin 3x
dx
cos x  1
0
215/I = 
2
2
216/I =
ln(1  x)
202/I = 
dx
x2
1
2

2
sin 2x
dx
1  cos x
0
sin 2008 x
dx
204/I = 
sin 2008 x  cos 2008 x
0

2
1 x
1 x2
217/I = 
dx
4
1 1 x
3

x2 1
dx
x2
1

4 sin 3
x
dx
207/I = 
cos 2 x
0

2
208/I =  cos 2 x.cos 4x dx
0
1
1
dx
2x
 ex
0e
e
ln x
dx
210/I = 
(x  1) 2
1
209/I = 
211/I = 
0
x3
7
218/I =

dx
1 x
1  ex
219/I = 
dx
x
0 1 e
0
ln 2
3
2
220/I =  x 1  x dx
0
1
0
e
1
dx
2
1
205/I =  sin x.ln(1  cos x) dx
206/I =

0
2
203/I = 

2
x2
1
dx
x 1  x
221/I =  x 2  1dx
0

2
222/I =  (cos3 x  sin 3 x) dx
0
3
x2 1
dx
223/I = 
x 1
0
1
224/I =  (1  x) 2 .e2x dx
0

2
225/I = 
0
7
3
226/I = 
0
.
cos x
cos x  1
2
x 1
dx
3
3x  1
dx

9. 
2 1  sin 2x
 cos 2x
dx
cos x  sin x
227/I = 

6
1
(1  e x )2
228/I = 
dx
1  e2x
0

2
sin 2x  sin x
dx
cos3x  1
0
242/I = 

4
sin 2x
dx
sin 2 x  2cos 2 x
0
243/I = 
3
229/I =  x 2 (1  x)3 dx
0

2
230/I =
2
2
244/I =
3
sin x.cos x
 cos2 x  1 dx
0
1
2
231/I = 
x 2  3x  2
0

2
2
245/I =
4x  1
1
246/I =
232*/I =  x sin x.cos xdx
0
247/I = 
cos x
233/I = 
dx
cos 2x  7
0
4
1
234/I =  2
dx
1 x (x  1)
0
2
248/I =
3
7

x x2  9
dx
0

2
3
 cos x cos x  cos xdx

1 x
2
dx
1 x2
dx
x2
x2
4x
1
2
dx
x x 1
2
dx
0

2
250/I = 
238/I =  x sin 3 x cos 4 xdx
239/I =
x3
dx
sin x
dx
1  sin x
0
236/I = 

1 x
2
249/I =  x 5 (1  x 3 )6 dx
0
2
237/I =

2
3
1
235/I =  sin 2x(1  sin x) dx
2

2
2
1

2
x 1
dx
3
0 3x  2
4
1

0
dx
2

2

0
x3

2
1
240*/I =  ln( x 2  a  x)dx
1

2
cos x
dx
0 7  cos 2x
4
1
dx
252/I = 
(1  x)x 2
1
2
x 1
dx
253/I =  3
3x  2
0
251/I = 

3
cos x  sin x
dx
3  sin 2x

254*/I = 

2
1  sin x
dx
241/I = 
(1  cos x)e x
0
4
.

10. 
2

2
 cos x cos x  cos xdx
255/I =

3

2
sin x
dx
cos 2 x  3
0
267/I = 
2
268/I =

3
256/I =  tg 4 xdx

4

2 1  sin x
257*/I = 
0 1  cos x
269/I =  sin x cos x(1  cos x) 2 dx
e x dx
1
258/I =  (1  x 2 )3 dx
0

4
259/I =  x.tg 2 xdx
0
2
1
dx
(4  x 2 ) 2
0
1
3x 2
dx
261/I = 
3
0 x 2
2
1  x5
262*/I = 
dx
x(1  x 5 )
1
260/I= 

3
cos x
dx
1  sin 2 x
0
263/I = 

3
sin 2 x
dx
264/I = 
cos6 x
0

6
sin x  sin 3 x
dx
265/I = 
cos 2x
0

2
1
dx
sin x 1  cos x

265/I = 
0

4
sin 4 x  cos 4 x
270/I = 
dx
0 sin x  cos x  1

4
sin 4 x  cos 4 x
271/I = 
dx
0 sin x  cos x  1

2
sin x cos x  cos x
dx
sin x  2
0
272/I = 
1
273/I = 
266/I =
.
1
 x 6 (1  x 2 ) dx
1
1
ex
dx
x3
x 3  2x 2  10x  1
274/I = 
dx
x 2  2x  9
0
1
x3
275/I =  2
dx
3
0 (x  1)
1
3
276/I =  3
dx
0 x 1
1 4
x 1
dx
277*/I =  6
x 1
0
1
x
dx
278/I = 
(2x  1)3
0
7
1
dx
279/I = 
2  x 1
2
a
1
3
3

0

2
sin x
dx
x
3
2
280/I =

1
2
.
1
x 1 x
2
dx

11. 1
281*/I = 
x ln(x  1  x 2 )
1 x
0
2
2
295/I =
dx
282/I =  (x  1) 2 ln x dx
296/I =
1

287/I = 
0

2
1
298/I = 
5  12x  4x
1
x  1 x
3
299/I =
2
dx

1 x
1
3
 1 x
1
1 1  x
dx
dx
2
x 1 x
x3
0x
1
1
1 (3  2x)
2
1

297*/I = 
3
3x
dx
2
x  2x  1
1
1
4x  1
285/I =  3
dx
2
0 x  2x  x  2
286/I =
x3
0
2
283/I =  x 2 ln(x  1) dx
1
2
x x 1
2
7
1
3
284/I = 

2
3
4
0
2
1
dx
2
dx
 1 x
2
dx

3
1
dx
4
 sin x cos x
300/I = 
dx
6

2
cos x
dx
cos x  1
0
cos x
dx
2  cos 2x
301/I = 
cos x  sin x
dx
3  sin 2x

302/I = 
288/I = 
0

2
289/I = 
4

2
290/I =  (cos3 x  sin 3 x)dx
0

2
291/I =  cos5 x sin 4 xdx
0

2
292/I =  cos 2x(sin 4 x  cos 4 x)dx

2
cos x
dx
2  cos x
0

2
sin x
dx
sin x  2
0
303/I = 

2
cos3 x
dx
304/I = 
cos x  1
0

2
305/I =
0
0

2
1
dx
2  sin x
0
293/I = 

2
1
dx
294/I = 
2  cos x
0
1
 2cos x  sin x  3 dx

2
cos x
 (1  cos x)2 dx
306/I =

3

4
307/I =  tg 3 x dx
0

12. 
4
1
1
308*/I = 
dx
3  e2x
1

sin 2 x
309*/I =  x
dx
3 1

321*/I =  tg 5 x dx
0

4
322/I =  cotg 3 x dx

2

6

3
sin x
310*/I = 
dx
cos x  sin x
0

2
323/I =
sin 4 x
311/I = 
dx
cos 4 x  sin 4 x
0

2
tgx
312*/I = 
1  ln (cos x)
2
0

4

4
dx
0

2
sin 5 x
325/I = 
dx
cos x  1
0
sin x
dx
cos x  sin x
0
1
1
314*/I =  x
dx
(e  1)(x 2  1)
1
313*/I = 
315*/I =  e
0
1
316*/I = 
0

2
3x 1
x

3
cos 2x
dx
1  cos 2 2x

326/I = 
6
dx

4
327*/I =  (
2
x 4
2
dx
0
1
319*/I = 

4
1
cos x cos 2 x  1
3
1
2
x  x3
dx
329*/I = 
x4
1
ln 3
ex
2 3
330/I =
tan x
t gx  1 2
) dx
tgx  1
x
dx
x 1
328*/I = 
cos3 x
dx
317*/I = 
cos 4  3cos 2 x  3
0
x
t 2et
318*/Tìm x> 0 sao cho 
dt  1
(t  2) 2
0

3
1
 2  tgx dx
324*/I =

2
1
4
 tg x dx

0
dx
(e  1) e  1

1
e4
331/I =
320*/I =  3x  6x  1dx
2

1
e

4
0
x
x
1
dx
x cos 2 (ln x  1)
333*/I =  ln(1  tgx)dx
0
.
dx