Download - 333 bÀi ToÁn tÍch PhÂn Luy n
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333BI TON TCH PHN LUYN THI I HC1/ Cho hm s : f(x)= x.sinx+x2 . Tm nguyn hm ca hm s g(x)= x.cosx
bit rng nguyn hm ny trit tiu khi x=kT 2/nh m hm s: F(x) = mx 3 +(3m+2)x2 -4x+3 l mt nguyn hm ca hm s:
f(x) = 3x2 +10x-4.
3/Tm h nguyn hm ca hm s: f(x)= cos3
x.sin8x.
TNH :
4/I =3
2
4
3tg xdx
T
T
5/I =
42
6(2cotg x 5) dx
T
T
6/I =2
0
1 cos xdx
1 cos x
T
7/ I = 2
0
T
sin2 x.cos2xdx
8/I = 3
0
T
(2cos2 x-3sin2 x)dx
9 / I =2
2
s i n ( x )4 d x
s i n ( x )4
T
T
T
T
10 / I =
3
6
T
T (tgx-cotgx)2
dx
11/ I =4
4
0
cos x dx
T
12 / I =2
3
0
sin x dx
T
13*/ I =3 32
3
sin x sin xcotgxdx
sinx
T
T
14/I =2
4
0
sin x dx
T
15/I = 3
4
22
2cos
2sin
1T
Txx dx
16/I = 4
6
cotg2x dx
17/I =22 sin x
4
e sin 2x dx
18/ I =
4
02
2
cos
xe
tgx
.
34/I =1
2 23
1dx
x 4 x
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19/ I = 2
4
4sin
1T
T xdx
20/ I = 4
0
6cos
1
xdx
21/I = dxxxnsix )cos(2cos44
2
0
T
22/ I =2
3
0
cos xdx
T
23/ I =32
0
4sin xdx
1 cosx
T
24/ I =1
3 2
0
x 1 x dx
25/I =1
5 2
0
x 1 x dx
26/I =1
0
xdx
2x 1
27/I =
1
x0
1
dxe 4
28/I =2
x1
1dx
1 e
29/I =2x2
x0
edx
e 1
30/I =x1
x0
edx
e 1
31/I =e
21
ln x dxx(ln x 1)
32/I =
7
3
30
x 1dx
3x 1
33/I =2
3 2
0
(x 3) x 6x 8 dx
.
35/I =4
22
1dx
x 16 x
36*/I =6
22 3
1dx
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 33
x 4dx
x
40*/I =22
22
x 1dx
x x 1
41/I =ln 2
x
0
e 1dx
42/I =1
0
1dx
3 2x
43/I =2
5
0
sin xdx
T
44*/I =3
0
1 dxcosx
T
45/I =2x1
x0
edx
e 1
46/I =ln3
x0
1dx
e 1
47/I =
4
2
6
1
dxsin x cot gx
T
T
48/I =3 2e
1
ln x 2 ln xdx
x
.
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49/I =e
1
sin(ln x)dx
x
50/I =1
3 4 5
0
x (x 1) dx
51/I =
12 3
0 (1 2x)(1 3x 3x ) dx
52/I =2
31
1dx
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
2x0
1dx
e 3
56/I =xln3
x 30
edx
(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
25
1dx
x x 4
60/I =4
0
xdx
1 cos 2x
61/I =
2xln5
xln 2
e dxe 1
62/I =2e
1
x 1.ln xdx
x
63/I =21
0
xdx
(x 1) x 1
64/I =2
0
sin x.sin2x.sin3xdx
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 =73
8 42
xdx
1 x 2x
68*/I =2
0
4cos x 3sin x 1dx
4sin x 3cos x 5
69/I =
9
31
x. 1 xdx
70/I =2
30
x 1dx
3x 2
71*/I = 6
0
xsin dx
2
72*/I =2
0
xdx
2 x 2 x
73/I =3 3 2
0
x . 1 x dx
74**/I =1
20
ln(1 x)dx
x 1
75/I =2
0
sinxdx
sin x cos x
76/I =
e
1 cos(ln x)dx
77*/I =2
2
0
4 x dx
78/I =2
1
xdx
1 x 1
.
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79/I =e
1
1 3ln x ln xdx
x
80/I =3
2
2
ln(x x)dx
81/I =
e2
1(ln x) dx
82/I =
2e
e
ln xdx
x
83/I =
2e
1
ln xdx
ln x
84/I =2
2
1
x ln(x 1)dx
85/I =3
23
1 dxx 3
86/I =1
20
1dx
4 x
87/I =
2
4
0
sin xdx
88/I =3
2
6
ln(sin x) dxcos x
89/I =2
1
cos(ln x)dx
90*/I =2
2
0
ln( 1 x x)dx
91*/I =3
22
1dx
x 1
92/I =38
1
x 1dx
x
93/I =33
21
xdx
x 16
.
94/I =6
20
cosxdx
6 5sin x sin x
T
95*/I =
2e
2e
1 1( )dx
ln xln x
96/I =
32
4 x 4 dx
97/I =2
3 2
1
x 2x x 2 dx
98/I =
34
4
cos 2x 1dx
T
T
99/I =0
cos x sin xdxT
100/I =2
0
1 sin xdxT
101/I =
34
4
sin 2x dx
T
T
102/I =
0
1 sin xdxT
103/I =1 3
2
1
ln(x x 1) dx
-
104*/I =2
0
xsinxdx
1 cos x
T
105*/I =1
2 x1
1dx
(x 1)(4 1)
106*/I =41
x1
xdx
1 2
107/I =
2
4
0
x sin xdx
T
108/I =
2
4
0
x cos xdx
T
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109/I =6
2
0
x.sin x cos xdx
T
110*/I =2 x1
20
x edx
(x 2)
111/I =2x 2
0 e sin xdx
T
112/I =2
2
1
1x ln(1 )dx
x
113/I =e
21e
ln xdx
(x 1)
114/I =
12
0
1 xx.ln dx
1 x
115/I =2t
1
ln xdx I 2
x
116/I =3
0
sin x.ln(cosx)dx
T
117/I =2e 2
1
cos (ln x)dx
T
118/I =4
0
1dx
cosx
T
119*/I =4
30
1dx
cos x
T
120/I = 21
3 x
0x e dx
121/I =22 sin x 3
0
e .sin x cos xdx
T
122/I =2
40
sin2xdx
1 cos x
T
123/I =1
20
3dx
x 4x 5
124/I =2
21
5dx
x 6x 9
125/I =1
2
5
1dx
2x 8x 26
126/I =1
0
2x 9dx
x 3
127/I =4
21
1dx
x (x 1)
128*/I =0
2
2
sin2xdx
(2 sin x)T
129/I =1
20
x 3dx
(x 1)(x 3x 2)
130/I =1
30
4xdx
(x 1)
131/I =1
4 20
1dx
(x 4x 3)
132/I =
33
20
sin xdx(sin x 3)
T
133/I =33
6
4sin xdx
1 cos x
T
T
134/I =3
2
6
1dx
cosx.sin x
T
T
135/I =3
0
sin x.tgxdx
T
136/I =3
4
1dx
sin2x
T
T
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137/I =34
2 2 50
sin xdx
(tg x 1) .cos x
T
138/I =3
2 2
3
1dx
sin x 9cos x
T
T
139/I =2
2
cos x 1dx
cos x 2
T
T
140/I =2
0
1 sin xdx
1 3cos x
T
141/I =
2
0
cosx
dxsin x cos x 1
T
142/I =4
21
1dx
x (x 1)
143/I =1
33
1dx
x 4 (x 4)
144/I =33
0
sin xdx
cosx
T
145/I =1
0
x 1 xdx
146/I =6
4
x 4 1. dx
x 2 x 2
147/I =0
21
1dx
x 2x 9
148/I =3
21
1dx
4x x
149/I =2
2
1
4x x 5 dx
150/I =2
22
2x 5dx
x 4x 13
151/I =1
x0
1dx
3 e
152/I =
14x 2x2
2x0
3e edx
1 e
153/I =4
27
1dx
x 9 x
154/I = 2 x 2
0
e sin xdx
T
155/I =42
4 40
cos xdx
cos x sin x
T
156/I =1
0
3dx
x 9 x
157/I =0xsinxdx
T
158/I = 2 2
0
x cos xdxT
159/I =1
0
cos x dx
160/I =1
0
sin x dx
161/I =
2
4
0
x sin x dx
T
162/I =
2
4
0
x cos x dx
T
163/I = 2
0
xcos xsin xdxT
164/I =6
2
0
xcos xsin xdx
T
165/I =4
x
1
e dx
166/I =4
3x
0
e sin 4x dx
T
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167/I = 2x 2
0
e sin x dxT
168/I =2 x1
20
x edx
(x 2)
169/I =e
1
(1 x) ln x dx
170/I =e
2
1
x ln x dx
171/I =
1
e2
1
ln x dx
172/I =e
1
x(2 ln x) dx
173/I =
2e
2e
1 1( )dxln xln x
174/I =2
2
1
(x x) ln x dx
175/I =2
2
1
1x ln(1 )dx
x
176/I =2
51
ln xdx
x
177/I =e
21e
ln xdx
(x 1)
178/I =
12
0
1 xx ln dx
1 x
179/I =2
3
cos x.ln(1 cos x)dx
T
T
180/22 sin x 3
0
e sin x cos x dx
T
181/I=2
40
sin2xdx
1 sin x
T
.
182/I =2
40
sin2xdx
1 cos x
T
183/I =2
21
5dx
x 6x 9
184/I =
21
0
x 3x 2
dxx 3
185/I =4
21
1dx
x (x 1)
186/I =1
20
ln(1 x)dx
x 1
187/I41
60
1 xdx
1 x
188/I =1
15 8
0x 1 x dx
189/I =x1
x x0
edx
e e
190/I=e
1e
ln x dx
191/I =2
sinx
0(e cos x)cos x dx
T
192/I =2
0
sin2x.cosxdx
1 cos x
T
193/I =2
0
sin 2x sin xdx
1 3cos x
T
194/I = 24
0
1 2sin x dx1 sin 2x
T
195/I =5 33
20
x 2xdx
x 1
196/I =3
2
4
tgxdx
cos x 1 cos x
T
T
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197/I =2
2
1
x 1( ) dxx 2
198/I =4
2
0
x.tg xdx
T
199/I =
5
3( x 2 x 2 )dx
200/I =4
1
2dx
x 5 4
201/I =2
1
xdx
x 2 2 x
202/I =2
21
ln(1 x)dx
x
203/I =2
0
sin2xdx
1 cos x
T
204/I =20082
2008 20080
sin xdx
sin x cos x
T
205/I =2
0
sin x.ln(1 cosx)dx
T
206/I =23
21
x 1dx
x
207/I =34
20
sin xdx
cos x
T
208/I =2
2
0
cos x.cos4xdx
T
209/I =1
2x x0
1dx
e e
210/I =e
21e
ln xdx
(x 1)
211/I =1
0
1dx
x 1 x
212/I =21
20
xdx
4 x
213/I =1
20
xdx
4 x
214/I =
142
20
x
dxx 1
215/I =2
0
sin3xdx
cos x 1
T
216/I =
222
20
xdx
1 x
217/I =22
41
1 xdx
1 x
218/I =37
3 20
xdx
1 x
219/I =xln 2
x0
1 edx
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
T
223/I =23
0
x 1dx
x 1
224/I =
1
2 2x0(1 x) .e dx
225/I =2
20
cosxdx
cos x 1
T
226/I =
7
3
30
x 1dx
3x 1
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227/I =2
6
1 sin 2x cos 2xdx
cos x sin x
T
T
228/I =x 21
2x0
(1 e )dx
1 e
229/I = 3 2 3
0
x (1 x) dx
230/I =32
20
sin x.cos xdx
cos x 1
T
231/I =
12
20
4x 1dx
x 3x 2
232*/I = 20
xsin x.cos xdx
T
233/I =2
0
cosxdx
cos 2x 7
T
234/I =4
21
1dx
x (x 1)
235/I =
22 3
0 sin 2x(1 sin x) dx
T
236/I =2
30
x 1dx
3x 2
237/I =4
27
1dx
x x 9
238/I = 3 4
0
x sin x cos xdxT
239/I =2 3
2
cos x cos x cos xdx
T
T
240*/I =1
2
1
ln( x a x)dx
241/I =2
x0
1 sin xdx
(1 cos x)e
T
242/I =2
0
sin 2x sin xdx
cos3x 1
T
243/I =4
2 2
0
sin2xdx
sin x 2cos x
T
244/I =
232
20
xdx
1 x
245/I =
232
20
xdx
1 x
246/I =21
2
22
1 xdx
x
247/I =21
20
xdx
4 x
248/I =2
22
3
1dx
x x 1
249/I =1
5 3 6
0
x (1 x ) dx
250/I =2
0
sinxdx
1 sin x
T
251/I =2
0
cosxdx
7 cos 2x
T
252/I =4
21
1dx
(1 x)x
253/I =2
30
x 1dx
3x 2
254*/I =3
4
cos x sin xdx
3 sin 2x
T
T
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255/I =2
3
2
cos x cos x cos xdx
T
T
256/I =3
4
4
tg xdx
T
T
257*/I =2
x
0
1 sin xe dx
1 cos x
T
258/I =1
2 3
0
(1 x ) dx
259/I =4
2
0
x.tg xdx
T
260/I=2
2 20
1dx
(4 x )
261/I =21
30
3xdx
x 2
262*/I =52
51
1 xdx
x(1 x )
263/I =3
20
cosx dx1 sin x
T
264/I =23
60
sin xdx
cos x
T
265/I =36
0
sin x sin xdx
cos2x
T
265/I =2
3
1dx
sin x 1 cos x
T
T
266/I =3
6 21
1dx
x (1 x )
.
267/I =2
20
sinxdx
cos x 3
T
268/I =
2
0
sin xdx
x
T
269/I = 2 2
0
sin xcos x(1 cos x) dx
T
270/I =4 44
0
sin x cos xdx
sin x cos x 1
T
271/I =4 44
0
sin x cos xdx
sin x cos x 1
T
272/I =2
0
sin x cos x cos xdx
sin x 2
T
273/I =
11 x
3a
edx
x
274/I =3 21
20
x 2x 10x 1dx
x 2x 9
275/I =31
2 30
x dx(x 1)
276/I =1
30
3dx
x 1
277*/I =41
60
x 1dx
x 1
278/I =1
3
0
xdx
(2x 1)
279/I =7
2
1dx
2 x 1
280/I =
32
21
2
1dx
x 1 x
.
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281*/I =21
20
x ln(x 1 x )dx
1 x
282/I =4
2
1
(x 1) ln xdx
283/I =3
2
0
x ln(x 1)dx
284/I =32
21
3xdx
x 2x 1
285/I =1
3 20
4x 1dx
x 2x x 2
286/I =
12
21
2
1dx
(3 2x) 5 12x 4x
287/I =1
0
1dx
x 1 x
288/I =2
0
cosxdx
2 cos 2x
T
289/I =2
4
cos x sin xdx
3 sin 2x
T
T
290/I =2
3 3
0
(cos x sin x)dx
T
291/I =2
5 4
0
cos x sin xdx
T
292/I =2
4 4
0
cos 2x(sin x cos x)dx
T
293/I =2
0
1dx
2 sin x
T
294/I =2
0
1dx
2 cos x
T
295/I =2
22
3
1dx
x x 1
296/I =37
3 20
xdx
1 x
297*/I =
2
31
1 dxx 1 x
298/I =31
20
xdx
x 1 x
299/I =1
21
1dx
1 x 1 x
300/I =3
4
6
1 dxsin x cos x
T
T
301/I =2
0
cosxdx
cos x 1
T
302/I =2
0
cosxdx
2 cos x
T
303/I =2
0
sinxdx
sin x 2
T
304/I =32
0
cos xdx
cos x 1
T
305/I =2
0
1dx
2cos x sin x 3
T
306/I =2
2
3
cosxdx
(1 cos x)
T
T
307/I =4
3
0
tg x dx
T
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.
308*/I =1
2x1
1dx
3 e
309*/I =2
x
sin xdx
3 1
T
T
310*/I =
2
0
sinx
dxcos x sin x
T
311/I =42
4 40
sin xdx
cos x sin x
T
312*/I =2
20
tgxdx
1 ln (cos x)
T
313*/I =2
0sinx dx
cos x sin x
T
314*/I =1
x 21
1dx
(e 1)(x 1)
315*/I =1
3x 1
0
e dx
316*/I =21
20
xdx
x 4
317*/I =32
4 20
cos xdx
cos 3cos x 3
T
318*/Tm x> 0 sao cho2 tx
20
t edt 1
(t 2)!
319*/I =3
2
4
tanxdx
cos x cos x 1
T
T
320*/I =1
2
0
3x 6x 1dx
321*/I =4
5
0
tg x dx
T
322/I =4
3
6
cotg x dx
T
T
323/I =3
4
4
tg x dx
T
T
324*/I =4
0
1dx
2 tgx
T
325/I =
52
0
sin x
dxcos x 1
T
326/I =3
2
6
cos2xdx
1 cos 2x
T
T
327*/I =4
2
0
t gx 1( ) dx
tgx 1
T
328*/I =
1
31
2
x dxx 1
329*/I =3 32
41
x xdx
x
330/I =xln3
x x0
edx
(e 1) e 1
331/I =
14e
21
e
1 dxx cos (ln x 1)
T
333*/I =4
0
ln(1 tgx)dx
T
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