333 bài toán tích phân luyện thi đại học môn Toán

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) = 3x
2
 +10x-4. 
3/Tìm họ nguyên hàm của hàm số: f(x)= cos 3 x.sin8x. 
TÍNH : 
4/I = 
3
2
4
3tg x dx


 
5/I = 
4
2
6
(2cotg x 5)dx


 
 6/I = 
2
0
1 cos x
dx
1 cos x



 
7/ I = 
2
0

sin
2 
x.cos
2
xdx 
 8/I = 
3
0

(2cos
2 
x-3sin
2 
x)dx 
9 / I = 
2
2
sin( x)
4 dx
sin( x)
4






 
10 / I = 

3
6


(tgx-cotgx)
2
 dx 
11/ I = 
4
4
0
cos x dx

 
12 / I = 
2
3
0
sin x dx

 
 13*/ I = 
3 32
3
sin x sin x
cot gx dx
sin x



 
14/I = 
2
4
0
sin x dx

 
 15/I = 
3
4
22
2
cos
2
sin
1


xx dx 
16/I = 
4
6


cotg2x dx 
17/I = 
22 sin x
4
e sin 2x dx


 
 18/ I = 
4
0
2
2
cos

x
e tgx
. 
34/I =
1
2 2
3
1
dx
x 4 x
 
19/ I = 
2
4
4sin
1

 x
 dx 
20/ I = 
4
0
6cos
1

x
 dx 
21/I = dxxxnsix )cos(2cos
44
2
0


22/ I = 
2
3
0
cos xdx

 
23/ I = 
32
0
4sin x
dx
1 cosx


 
24/ I = 
1
3 2
0
x 1 x dx 
 25/I =
1
5 2
0
x 1 x dx 
26/I =
1
0
x
dx
2x 1
 
27/I =
1
x
0
1
dx
e 4
 
28/I =
2
x
1
1
dx
1 e
 
29/I =
2x2
x
0
e
dx
e 1
 
30/I =
x1
x
0
e
dx
e 1

 
 
31/I =
e
2
1
ln x
dx
x(ln x 1)
 
32/I =
7
3
3
0
x 1
dx
3x 1


 
33/I =
2
3 2
0
(x 3) x 6x 8 dx   
. 
35/I =
4
2
2
1
dx
x 16 x
 
36*/I =
6
2
2 3
1
dx
x x 9
 
37/I =
2
2 2
1
x 4 x dx

 
38/I =
2
2 3
0
x (x 4) dx 
39/I =
24
4 3
3
x 4
dx
x

 
40*/I =
22
2
2
x 1
dx
x x 1




 
41/I =
ln 2
x
0
e 1dx 
42/I =
1
0
1
dx
3 2x
 
43/I =
2
5
0
sin xdx

 
44*/I =
3
0
1
dx
cos x

 
45/I =
2x1
x
0
e
dx
e 1

 
 
46/I =
ln 3
x
0
1
dx
e 1
 
47/I =
4
2
6
1
dx
sin x cot gx


 
48/I =
3 2e
1
ln x 2 ln x
dx
x

 
. 
 49/I =
e
1
sin(ln x)
dx
x
 
50/I =
1
3 4 5
0
x (x 1) dx 
51/I =
1
2 3
0
(1 2x)(1 3x 3x ) dx   
52/I =
2
3
1
1
dx
x 1 x
 
53/I =
3
2 2
6
tg x cot g x 2dx


  
54/I =
1
2 3
0
(1 x ) dx 
55*/I =
1
2x
0
1
dx
e 3
 
56/I =
xln 3
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

 
59*/I =
2 3
2
5
1
dx
x x 4
 
60/I =
4
0
x
dx
1 cos2x


 
61/I =
2xln 5
x
ln 2
e
dx
e 1
 
62/I =
2e
1
x 1
.ln xdx
x

 
63/I =
21
0
x
dx
(x 1) x 1 
 
64/I =
2
0
sin x.sin 2x.sin3xdx

 
65/I =
2
4 4
0
cos2x(sin x cos x)dx

 
66*/I =
2
3 3
0
( cos x sin x)dx

 
67/I =
73
8 4
2
x
dx
1 x 2x 
 
68*/I =
2
0
4cos x 3sin x 1
dx
4sin x 3cos x 5

 
 
 
69/I =
9
3
1
x. 1 xdx 
70/I =
2
3
0
x 1
dx
3x 2


 
71*/I =
6
0
x
sin dx
2

 
72*/I =
2
0
x
dx
2 x 2 x  
 
73/I =
3
3 2
0
x . 1 x dx 
74**/I =
1
2
0
ln(1 x)
dx
x 1


 
75/I =
2
0
sin x
dx
sin x cos x


 
76/I =
e
1
cos(ln x)dx

 
77*/I =
2
2
0
4 x dx 
78/I =
2
1
x
dx
1 x 1 
 
. 
79/I =
e
1
1 3ln x ln x
dx
x

 
80/I =
3
2
2
ln(x x)dx 
81/I =
e
2
1
(ln x) dx 
82/I =
2e
e
ln x
dx
x
 
83/I =
2e
1
ln x
dx
ln x
 
84/I =
2
2
1
x ln(x 1)dx 
85/I =
3
2
3
1
dx
x 3
 
86/I =
1
2
0
1
dx
4 x
 
87/I =
2
4
0
sin xdx

 
88/I =
3
2
6
ln(sin x)
dx
cos x


 
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
 
92/I =
38
1
x 1
dx
x

 
93/I =
33
2
1
x
dx
x 16
 
. 
94/I =
6
2
0
cos x
dx
6 5sin x sin x

 
 
95*/I =
2e
2
e
1 1
( )dx
ln xln 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
cos 2x 1dx


 
99/I =
0
cos x sin xdx

 
100/I =
2
0
1 sin xdx

 
101/I =
3
4
4
sin 2x dx


 
102/I =
0
1 sin xdx

 
103/I =
1 3
2
1
ln(x x 1) dx

  
  
104*/I =
2
0
xsin x
dx
1 cos x


 
105*/I =
1
2 x
1
1
dx
(x 1)(4 1)  
 
106*/I =
41
x
1
x
dx
1 2 
 
107/I =
2
4
0
x sin xdx

 
108/I =
2
4
0
x cos xdx

 
109/I =
6
2
0
x.sin x cos xdx

 
110*/I =
2 x1
2
0
x e
dx
(x 2)
 
111/I =
2x 2
0
e sin xdx

 
112/I =
2
2
1
1
x ln(1 )dx
x
 
113/I =
e
2
1
e
ln x
dx
(x 1)
 
114/I =
1
2
0
1 x
x.ln dx
1 x


 
115/I =
2t
1
ln x
dx I 2
x
 
  
 
 
116/I =
3
0
sin x.ln(cos x)dx

 
117/I =
2e
2
1
cos (ln x)dx

 
118/I =
4
0
1
dx
cos x

 
119*/I =
4
3
0
1
dx
cos x

 
120/I =
2
1
3 x
0
x e dx 
121/I =
22 sin x 3
0
e .sin x cos xdx

 
122/I =
2
4
0
sin 2x
dx
1 cos x


 
123/I =
1
2
0
3
dx
x 4x 5 
 
124/I =
2
2
1
5
dx
x 6x 9 
 
125/I =
1
2
5
1
dx
2x 8x 26  
 
126/I =
1
0
2x 9
dx
x 3


 
127/I =
4
2
1
1
dx
x (x 1)
 
128*/I =
0
2
2
sin 2x
dx
(2 sin x) 
 
129/I =
1
2
0
x 3
dx
(x 1)(x 3x 2)

  
 
130/I =
1
3
0
4x
dx
(x 1)
 
131/I =
1
4 2
0
1
dx
(x 4x 3) 
 
132/I =
33
2
0
sin x
dx
(sin x 3)


 
133/I =
33
6
4sin x
dx
1 cos x

 
 
134/I =
3
2
6
1
dx
cos x.sin x


 
135/I =
3
0
sin x.tgxdx

 
136/I = 
3
4
1
dx
sin 2x


 
. 
137/I = 
34
2 2 5
0
sin x
dx
(tg x 1) .cos x


 
138/I =
3
2 2
3
1
dx
sin x 9cos x




 
139/I =
2
2
cos x 1
dx
cos x 2





 
140/I = 
2
0
1 sin x
dx
1 3cos x



 
141/I =
2
0
cos x
dx
sin x cos x 1

 
 
142/I = 
4
2
1
1
dx
x (x 1)
 
143/I =
1
3
3
1
dx
x 4 (x 4)   
 
144/I =
33
0
sin x
dx
cos x

 
145/I =
1
0
x 1 xdx 
146/I =
6
4
x 4 1
. dx
x 2 x 2

 
 
147/I = 
0
2
1
1
dx
x 2x 9  
 
148/I =
3
2
1
1
dx
4x x
 
149/I = 
2
2
1
4x x 5 dx

  
150/I = 
2
2
2
2x 5
dx
x 4x 13

 
 
151/I =
1
x
0
1
dx
3 e
 
152/I = 
1
4x 2x2
2x
0
3e e
dx
1 e


 
153/I =
4
2
7
1
dx
x 9 x
 
154/I = 
2
x 2
0
e sin xdx

 
155/I = 
42
4 4
0
cos x
dx
cos x sin x


 
156/I =
1
0
3
dx
x 9 x 
 
157/I = 
0
xsin xdx

 
158/I =
2 2
0
x cos xdx

 
159/I =
1
0
cos x dx 
160/I =
1
0
sin x dx 
161/I = 
2
4
0
x sin x dx

 
162/I =
2
4
0
x cos x dx

 
163/I =
2
0
x cos xsin x dx

 
164/I = 
6
2
0
x cos xsin x dx

 
165/I =
4
x
1
e dx 
166/I =
4
3x
0
e sin 4x dx

 
167/I =
2x 2
0
e sin x dx

 
168/I =
2 x1
2
0
x e
dx
(x 2)
 
169/I =
e
1
(1 x) ln x dx 
170/I =
e
2
1
x ln x dx 
171/I =
1
e
2
1
ln x dx 
172/I =
e
1
x(2 ln x)dx 
173/I =
2e
2
e
1 1
( )dx
ln xln x
 
174/I =
2
2
1
(x x)ln x dx 
175/I =
2
2
1
1
x ln(1 )dx
x
 
176/I =
2
5
1
ln x
dx
x
 
177/I =
e
2
1
e
ln x
dx
(x 1)
 
178/I =
1
2
0
1 x
x ln dx
1 x


 
179/I =
2
3
cos x.ln(1 cos x)dx


 
180/
22 sin x 3
0
e sin x cos x dx

 
181/I= 
2
4
0
sin 2x
dx
1 sin x


 
. 
182/I =
2
4
0
sin 2x
dx
1 cos x


 
183/I =
2
2
1
5
dx
x 6x 9 
 
184/I =
21
0
x 3x 2
dx
x 3
 

 
185/I =
4
2
1
1
dx
x (x 1)
 
186/I =
1
2
0
ln(1 x)
dx
x 1


 
187/I
41
6
0
1 x
dx
1 x


 
188/I =
1
15 8
0
x 1 x dx 
189/I =
x1
x x
0
e
dx
e e
 
190/I= 
e
1
e
ln x dx 
191/I =
2
sin x
0
(e cos x)cos x dx

 
192/I =
2
0
sin 2x.cos x
dx
1 cos x


 
193/I =
2
0
sin 2x sin x
dx
1 3cos x



 
194/I =
24
0
1 2sin x
dx
1 sin 2x



 
195/I = 
5 33
2
0
x 2x
dx
x 1


 
196/I =
3
2
4
tgx
dx
cos x 1 cos x

 
 
197/I =
2
2
1
x 1
( ) dx
x 2


 
198/I =
4
2
0
x.tg x dx

 
199/I =
5
3
( x 2 x 2 )dx

   
200/I =
4
1
2
dx
x 5 4  
 
201/I =
2
1
x
dx
x 2 2 x  
 
202/I =
2
2
1
ln(1 x)
dx
x

 
203/I =
2
0
sin 2x
dx
1 cos x


 
204/I =
20082
2008 2008
0
sin x
dx
sin x cos x


 
205/I =
2
0
sin x.ln(1 cos x)dx

 
206/I =
23
2
1
x 1
dx
x

 
207/I =
34
2
0
sin x
dx
cos x

 
208/I =
2
2
0
cos x.cos4x dx

 
209/I =
1
2x x
0
1
dx
e e
 
210/I =
e
2
1
e
ln x
dx
(x 1)
 
211/I =
1
0
1
dx
x 1 x 
 
212/I =
21
2
0
x
dx
4 x
 
213/I =
1
2
0
x
dx
4 x
 
214/I =
1
42
2
0
x
dx
x 1
 
215/I =
2
0
sin 3x
dx
cos x 1


 
216/I =
2
22
2
0
x
dx
1 x
 
217/I =
22
4
1
1 x
dx
1 x


 
218/I =
37
3 2
0
x
dx
1 x
 
219/I =
xln 2
x
0
1 e
dx
1 e


 
220/I =
1
0
x 1 x dx 
221/I =
1
2
0
x 1dx 
222/I =
2
3 3
0
(cos x sin x)dx

 
223/I =
23
0
x 1
dx
x 1


 
224/I =
1
2 2x
0
(1 x) .e dx 
225/I =
2
2
0
cos x
dx
cos x 1


 
226/I =
7
3
3
0
x 1
dx
3x 1


 
. 
227/I =
2
6
1 sin 2x cos2x
dx
cos x sin x


 

 
228/I =
x 21
2x
0
(1 e )
dx
1 e


 
229/I =
3
2 3
0
x (1 x) dx 
230/I = 
32
2
0
sin x.cos x
dx
cos x 1


 
231/I =
1
2
2
0
4x 1
dx
x 3x 2

 
 
232*/I =
2
0
xsin x.cos xdx

 
233/I =
2
0
cos x
dx
cos 2x 7


 
234/I =
4
2
1
1
dx
x (x 1)
 
235/I =
2
2 3
0
sin 2x(1 sin x) dx

 
236/I =
2
3
0
x 1
dx
3x 2


 
237/I =
4
2
7
1
dx
x x 9
 
238/I =
3 4
0
xsin x cos xdx

 
239/I =
2
3
2
cos x cos x cos xdx



 
240*/I =
1
2
1
ln( x a x)dx

  
241/I =
2
x
0
1 sin x
dx
(1 cos x)e



 
242/I =
2
0
sin 2x sin x
dx
cos3x 1



 
243/I =
4
2 2
0
sin 2x
dx
sin x 2cos x


 
244/I =
2
32
2
0
x
dx
1 x
 
245/I =
2
32
2
0
x
dx
1 x
 
246/I =
21
2
2
2
1 x
dx
x

 
247/I =
21
2
0
x
dx
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


 
251/I =
2
0
cos x
dx
7 cos 2x


 
252/I =
4
2
1
1
dx
(1 x)x
 
253/I =
2
3
0
x 1
dx
3x 2


 
254*/I =
3
4
cos x sin x
dx
3 sin 2x




 
 . 
 255/I =
2
3
2
cos x cos x cos xdx



 
256/I =
3
4
4
tg xdx


 
257*/I =
2
x
0
1 sin x
e dx
1 cos x



 
258/I =
1
2 3
0
(1 x ) dx 
259/I =
4
2
0
x.tg xdx

 
260/I=
2
2 2
0
1
dx
(4 x )
 
261/I = 
21
3
0
3x
dx
x 2
 
262*/I = 
52
5
1
1 x
dx
x(1 x )


 
263/I =
3
2
0
cos x
dx
1 sin x


 
264/I =
23
6
0
sin x
dx
cos x

 
265/I =
36
0
sin x sin x
dx
cos2x


 
265/I =
2
3
1
dx
sin x 1 cos x

 
 
266/I =
3
6 2
1
1
dx
x (1 x )
 
. 
267/I =
2
2
0
sin x
dx
cos x 3


 
268/I =
2
0
sin x
dx
x

 
269/I =
2
2
0
sin x cos x(1 cos x) dx

 
270/I =
4 44
0
sin x cos x
dx
sin x cos x 1


 
 
271/I =
4 44
0
sin x cos x
dx
sin x cos x 1


 
 
272/I =
2
0
sin x cos x cos x
dx
sin x 2



 
273/I =
1
1 x
3
a
e
dx
x
 
274/I =
3 21
2
0
x 2x 10x 1
dx
x 2x 9
  
 
 
275/I =
31
2 3
0
x
dx
(x 1)
 
276/I =
1
3
0
3
dx
x 1
 
277*/I =
41
6
0
x 1
dx
x 1


 
278/I =
1
3
0
x
dx
(2x 1)
 
279/I =
7
2
1
dx
2 x 1 
 
280/I =
3
2
2
1
2
1
dx
x 1 x
 
. 
281*/I =
21
2
0
x ln(x 1 x )
dx
1 x
 

 
282/I =
4
2
1
(x 1) ln x dx 
283/I =
3
2
0
x ln(x 1)dx 
284/I =
32
2
1
3x
dx
x 2x 1 
 
285/I =
1
3 2
0
4x 1
dx
x 2x x 2

  
 
286/I = 
1
2
2
1
2
1
dx
(3 2x) 5 12x 4x   
 
287/I =
1
0
1
dx
x 1 x 
 
288/I =
2
0
cos x
dx
2 cos 2x


 
289/I =
2
4
cos x sin x
dx
3 sin 2x




 
290/I =
2
3 3
0
(cos x sin x)dx

 
291/I =
2
5 4
0
cos xsin xdx

 
292/I =
2
4 4
0
cos2x(sin x cos x)dx

 
293/I =
2
0
1
dx
2 sin x


 
294/I =
2
0
1
dx
2 cos x


 
295/I =
2
2
2
3
1
dx
x x 1
 
296/I =
37
3 2
0
x
dx
1 x
 
297*/I =
2
3
1
1
dx
x 1 x
 
298/I =
31
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 cos x


 
301/I =
2
0
cos x
dx
cos x 1


 
302/I =
2
0
cos x
dx
2 cos x


 
303/I =
2
0
sin x
dx
sin x 2


 
304/I =
32
0
cos x
dx
cos x 1


 
305/I = 
2
0
1
dx
2cos x sin x 3

 
 
306/I = 
2
2
3
cos x
dx
(1 cos x)

 
 
307/I =
4
3
0
tg x dx

 
. 
308*/I =
1
2x
1
1
dx
3 e 
 
309*/I =
2
x
sin x
dx
3 1

 
 
310*/I =
2
0
sin x
dx
cos x sin x


 
311/I =
42
4 4
0
sin x
dx
cos x sin x


 
312*/I =
2
2
0
tgx
dx
1 ln (cos x)


 
313*/I =
2
0
sin x
dx
cos x sin x


 
314*/I =
1
x 2
1
1
dx
(e 1)(x 1)  
 
315*/I =
1
3x 1
0
e dx 
316*/I =
21
2
0
x
dx
x 4
 
317*/I =
32
4 2
0
cos x
dx
cos 3cos x 3

 
 
318*/Tìm x> 0 sao cho 
2 tx
2
0
t e
dt 1
(t 2)


 
319*/I =
3
2
4
tan x
dx
cos x cos x 1

 
 
320*/I =
1
2
0
3x 6x 1dx   
321*/I =
4
5
0
tg x dx

 
322/I =
4
3
6
cotg x dx


 
323/I = 
3
4
4
tg x dx


 
324*/I = 
4
0
1
dx
2 tgx


 
325/I =
52
0
sin x
dx
cos x 1


 
326/I =
3
2
6
cos 2x
dx
1 cos 2x

 
 
327*/I =
4
2
0
t gx 1
( ) dx
tgx 1



 
328*/I =
1
3
1
2
x
dx
x 1
 
329*/I =
3 32
4
1
x x
dx
x

 
330/I =
xln 3
x x
0
e
dx
(e 1) e 1 
 
331/I =
1
4e
2
1
e
1
dx
x cos (ln x 1)



 
333*/I =
4
0
ln(1 tgx)dx

