Download Các bài toán về tích phân luyện thi đại học
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<span class='text_page_counter'>(1)</span><div class='page_container' data-page=1>
<b>333</b>
<b> </b>
<b> BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC</b>
<sub></sub>
1/ Cho hàm số : f(x)= x.sinx+x2<sub> . Tìm nguyên hàm của hàm số g(x)= x.cosx </sub>
biết rằng nguyên hàm này triệt tiêu khi x=k <i>π</i>
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<sub> +10x-4.</sub>
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 =
<sub></sub>
0
<i>π</i>
2
❑ sin2 x.cos2xdx
8/I =
<sub></sub>
0
<i>π</i>
3
❑ (2cos2 x-3sin2 x)dx
9 / I =
2
2
sin( x)
4 <sub>dx</sub>
sin( x)
4
10 / I =
<i>−π</i>
6
<i>π</i>
3
❑ (tgx-cotgx)2 dx
11/ I =
4
4
0
cos x dx
19/ I =
<i>π</i>
4
<i>π</i>
2
1
sin4<i><sub>x</sub></i> dx
12 / I =
2
3
0
sin x dx
13*/ I =
3 3
2
3
sin x sin x
cot gx dx
sin x
14/I =
2
4
0
sin x dx
15/I =
<i>π</i>
4
<i>π</i>
3
1
sin2<i>x</i>
2cos
2<i>x</i>
2
dx
16/I =
<sub></sub>
<i>π</i>
6
<i>π</i>
4
❑ cotg2x dx
17/I =
2
2
sin x
4
e sin 2x dx
18/ I =
<sub></sub>
0
<i>π</i>
4
<i>e</i>tgx+2
cos2<i><sub>x</sub></i>
<b>.</b>
34/I =
1
2 2
3
1
dx
x 4 x
</div>
<span class='text_page_counter'>(2)</span><div class='page_container' data-page=2>
20/ I =
<sub></sub>
0
<i>π</i>
4
1
cos6<i><sub>x</sub></i> dx
21/I =
si
cos 2<i>x</i>(¿<i>n</i>4<i>x</i>+cos4<i>x</i>)dx
0
<i>π</i>
2
¿
22/ I =
2
3
0
cos xdx
23/ I =
3
2
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 =
2x
2
x
0
e
dx
e 1
30/I =
x
1
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
<b>.</b>
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 =
2
4
4 3
3
x 4
dx
x
40*/I =
2
2
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 =
2x
1
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 2
e
1
ln x 2 ln x
dx
x
</div>
<span class='text_page_counter'>(3)</span><div class='page_container' data-page=3>
49/I =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 <sub>dx</sub>
e 3
56/I =
x
ln 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 cos 2x
61/I =
2x
ln 5
x
ln 2
e
dx
e 1
62/I =
2
e
1
x 1
.ln xdx
x
63/I =
2
1
0
x <sub>dx</sub>
(x 1) x 1
64/I =
2
0
sin x.sin 2x.sin 3xdx
65/I =
2
4 4
0
cos 2x(sin x cos x)dx
66*/I =
2
3 3
0
( cos x sin x )dx
67/I =
7
3
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
</div>
<span class='text_page_counter'>(4)</span><div class='page_container' data-page=4>
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 =
2
e
e
ln x
dx
x
83/I =
2
e
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 =
3
8
1
x 1
dx
x
<b>.</b>
94/I =
6
2
0
cos x
dx
6 5sin x sin x
95*/I =
2
e
2
e
1 1
( )dx
ln x
ln 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
<sub></sub> <sub></sub>
104*/I =0 2
x sin x
dx
1 cos x
105*/I =
1
2 x
1
1
dx
(x 1)(4 1)
106*/I =
4
1
x
1
x
dx
1 2
2
4
x sin xdx
</div>
<span class='text_page_counter'>(5)</span><div class='page_container' data-page=5>
93/I =1 2
x
dx
x 16
<b>.</b>
109/I =
6
2
0
x.sin x cos xdx
110*/I =
2 x
1
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 =
2
t
1
ln x
dx I 2
x
116/I =
3
0
sin x.ln(cos x)dx
117/I =
2
e
2
1
cos (ln x)dx
upload.123doc.net/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
108/I =
4
0
x cos xdx
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 =
3
3
2
0
sin x <sub>dx</sub>
(sin x 3)
133/I =
3
3
6
4sin x
dx
1 cos x
134/I =
3
2
6
1
dx
cos x.sin x
</div>
<span class='text_page_counter'>(6)</span><div class='page_container' data-page=6>
121/I =
2
2
sin x 3
0
e .sin x cos xdx
122/I =
2
4
0
sin 2x
dx
1 cos x
137/I =
3
4
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 =
3
3
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
135/I =
3
0
sin x.tgxdx
136/I =
3
4
1
dx
sin 2x
<b>.</b>
152/I =
1
4x 2x
2
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 =
4
2
4 4
0
cos x
dx
cos x sin x
156/I =
1
0
3
dx
x 9 x
157/I = 0
x sin 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
</div>
<span class='text_page_counter'>(7)</span><div class='page_container' data-page=7>
148/I =1 2
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
167/I =
2x 2
0
e sin x dx
168/I =
2 x
1
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 =
2
e
2
e
1 1
( )dx
ln x
ln 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)
163/I =
2
0
x cos x sin x dx
164/I =
6
2
0
x cos x sin x dx
165/I =
4
x
1
e dx
166/I =
4
3x
0
e sin 4x dx
182/I =
2
4
0
sin 2x
dx
1 cos x
183/I =
2
2
1
5
dx
x 6x 9
184/I =
2
1
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
4
1
6
0
1 x
dx
1 x
188/I =
1
15 8
0
x 1 x dx
189/I =
x
1
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
</div>
<span class='text_page_counter'>(8)</span><div class='page_container' data-page=8>
178/I =
1
2
0
1 x
x ln dx
1 x
179/I =
2
3
cos x.ln(1 cos x)dx
180/
2
2
sin x 3
0
e sin x cos x dx
181/I=
2
4
0
sin 2x
dx
1 sin x
<b>.</b>
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 =
2008
2
2008 2008
0
sin x
dx
sin x cos x
205/I =
2
0
sin x.ln(1 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 =
2
4
0
1 2sin x
dx
1 sin 2x
195/I =
5 3
3
2
0
x 2x
dx
x 1
196/I =
3
2
4
tgx
dx
cos x 1 cos x
212/I =
2
1
2
0
x
dx
4 x
213/I =
1
2
0
x
dx
4 x
214/I =
1
4
2
2
0
x
dx
x 1
215/I =
2
0
sin 3x
dx
cos x 1
216/I =
2
2
2
2
0
x
dx
1 x
217/I =
2
2
4
1
1 x
dx
1 x
218/I =
3
7
3 2
0
x
dx
1 x
219/I =
x
ln 2
x
0
1 e
dx
1 e
</div>
<span class='text_page_counter'>(9)</span><div class='page_container' data-page=9>
206/I = 1 2
x 1
dx
x
207/I =
3
4
2
0
sin x
dx
cos x
208/I =
2
2
0
cos x.cos 4x 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
227/I =
2
6
1 sin 2x cos 2x
dx
cos x sin x
228/I =
x 2
1
2x
0
(1 e )
dx
1 e
229/I =
3
2 3
0
x (1 x) dx
230/I =
3
2
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
x sin x.cos xdx
233/I =
2
0
cos x
dx
cos 2x 7
234/I =
4
2
1
1
dx
x (x 1)
220/I =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 =
2
3
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
<b>.</b>
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
3
2
2
0
x
dx
1 x
245/I =
2
3
2
2
0
x
dx
1 x
246/I =
2
1
2
2
2
1 x
dx
x
247/I =
2
1
2
0
x
dx
4 x
</div>
<span class='text_page_counter'>(10)</span><div class='page_container' data-page=10>
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
x sin 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
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 )
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
<b> .</b>
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 4
4
0
sin x cos x
dx
sin x cos x 1
271/I =
4 4
4
0
sin x cos x
dx
sin x cos x 1
</div>
<span class='text_page_counter'>(11)</span><div class='page_container' data-page=11>
261/I = 0 3
3x
dx
x 2
262*/I =
5
2
5
1
1 x
dx
x(1 x )
263/I =
3
2
0
cos x
dx
1 sin x
264/I =
2
3
6
0
sin x
dx
cos x
265/I =
3
6
0
sin x sin x
dx
cos 2x
265/I =
2
3
1
dx
sin x 1 cos x
266/I =
3
6 2
1
1
dx
x (1 x )
<b>.</b>
281*/I =
2
1
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 =
3
2
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
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 2
1
2
0
x 2x 10x 1
dx
x 2x 9
275/I =
3
1
2 3
0
x
dx
(x 1)
276/I =
1
3
0
3
dx
x 1
277*/I =
4
1
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
<b>.</b>
295/I =
2
2
2
3
1
dx
x x 1
296/I =
3
7
3 2
0
x
dx
1 x
297*/I =
2
3
1
1
dx
x 1 x
298/I =
3
1
2
0
x
dx
x 1 x
299/I =
1
2
1
1
dx
1 x 1 x
</div>
<span class='text_page_counter'>(12)</span><div class='page_container' data-page=12>
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 x sin xdx
292/I =
2
4 4
0
cos 2x(sin x cos x)dx
293/I =
2
0
1
dx
2 sin x
294/I =
2
0
1
dx
2 cos x
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 =
4
2
4 4
0
sin x
dx
cos x sin x
2
2
0
tgx
dx
1 ln (cos 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 =
3
2
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
321*/I =
4
5
0
tg x dx
322/I =
4
3
6
cotg x dx
323/I =
3
4
4
tg x dx
</div>
<span class='text_page_counter'>(13)</span><div class='page_container' data-page=13>
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 =
2
1
2
0
x
dx
x 4
317*/I =
3
2
4 2
0
cos x
dx
cos 3cos x 3
318*/Tìm x> 0 sao cho
2 t
x
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
324*/I =
4
0
1
dx
2 tgx
325/I =
5
2
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 3
2
4
1
x x
dx
x
330/I =
x
ln 3
x x
0
e
dx
(e 1) e 1
331/I =
1
4
e
2
1
e
1
dx
x cos (ln x 1)
333*/I =
4
0
ln(1 tgx)dx
</div>
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