[r]
(1)333 BÀI TỐN TÍCH PHÂN LUYỆN THI ĐẠI HỌc
1/ Cho hàm số : f(x)= x.sinx+x2 Tìm nguyên hàm hàm số g(x)= x.cosx
biết nguyên hàm triệt tiêu x=k
2/Định m để hàm số: F(x) = mx3+(3m+2)x2 -4x+3 nguyên hàm hàm số:
f(x) = 3x2 +10x-4.
3/Tìm họ nguyên hàm hàm số: f(x)= cos3x.sin8x.
TÍNH :
4/I =
4
3tg x dx
5/I =
4
2
6
(2cotg x 5)dx
6/I =
0
1 cos x dx
1 cos x
7/ I =2
sin2 x.cos2xdx
8/I = 3
(2cos2 x-3sin2 x)dx
9 / I =
2
2
sin( x)
4 dx
sin( x)
4
10 / I =
3
6
(tgx-cotgx)2 dx
11/ I = 4
cos x dx
19/ I =
4 sin
1
x
dx
20/ I = 4
6 cos
1
x dx
12 / I =
sin x dx
13*/ I =
3
3
sin x sin x
cot gx dx sin x
14/I =
sin x dx
15/I =
4
2
2 cos sin
1
x x
dx
16/I =
6
cotg2x dx
17/I = sin x2
4
e sin 2x dx
18/ I = 4
2 cos
x etgx
34/I =
1
2
3
1 dx
x x
35/I =
4
2
1 dx
x 16 x
36*/I =
6
2
1 dx
x x
37/I = 2
1
x x dx
(2)21/I = 2cos2x(sin4x cos4 x)dx
0
22/ I =
cos xdx
23/ I =
0
4sin x dx cosx
24/ I =
1
3
0
x x dx
25/I =
1
5
0
x x dx
26/I =
1
0
x
dx 2x 1
27/I =
1 x
1 dx
e 4
28/I =
2
x
1 dx e 29/I =
2x
x
e
dx
e 1
30/I =
x
x
e
dx
e
31/I =
e
2
ln x
dx
x(ln x 1)
32/I =
7
3
x dx 3x
33/I =
2
3
(x 3) x 6x dx
49/I =
e
1
sin(ln x) dx x
50/I =
1
3
x (x 1) dx
51/I =
1
2
(1 2x)(1 3x 3x ) dx
38/I =
2
2
x (x 4) dx
39/I =
2
4 3
x
dx x
40*/I =
2
2
x
dx
x x
41/I =
ln x
e 1dx
42/I =
1
0
1
dx 2x
43/I =2
sin xdx
44*/I =3
0
1 dx cos x
45/I =
2x
x
e
dx
e
46/I =
ln
x
1
dx
e 1
47/I =
4
1
dx sin x cot gx
48/I =
3
e
1
ln x ln x dx x
64/I =2
0
sin x.sin 2x.sin 3xdx
65/I =2 4
0
cos 2x(sin x cos x)dx
66*/I =2 3
0
( cos x sin x )dx
67/I =
7
8
x
dx
1 x 2x
(3)52/I =
2
3
1
dx
x x
53/I =
3
2
6
tg x cot g x 2dx
54/I =
1
2
(1 x ) dx
55*/I =
1 2x
1 dx
e 3
56/I =
x ln
x
e
dx
(e 1)
57/I =
0
2x
x(e x 1)dx
58/I =26
0
1 cos x sin x.cos xdx
59*/I =
2
2
1
dx
x x 4
60/I =4
0
x
dx cos 2x
61/I =
2x ln
x ln
e
dx
e
62/I =
2 e
1
x
.ln xdx x
63/I =
2
0
x
dx (x 1) x 1
79/I =
e
1
1 3ln x ln x dx x
80/I =
3 2
ln(x x)dx
81/I =
e
2
(ln x) dx
68*/I =2
0
4cos x 3sin x dx 4sin x 3cos x
69/I =
9
x xdx
70/I =
2
x dx 3x
71*/I =
0
x
sin dx
2
72*/I =
2
0
x
dx
2 x x
73/I =
3
3
0
x x dx
74**/I =
1
ln(1 x) dx
x
75/I =2
0
sin x
dx sin x cos x
76/I =e
1
cos(ln x)dx
77*/I =
2
2
4 x dx
78/I =
2
1
x
dx
1 x 1
94/I =6
2
cos x
dx 5sin x sin x
95*/I =
2 e
2 e
1
( )dx
ln x
ln x
96/I =
3
x dx
97/I =
2
3
x 2x x dx
98/I =
3
4
cos 2x 1dx
(4)82/I =
2 e
e
ln x dx x
83/I =
2 e
1
ln x dx ln x
84/I =
2
2
x ln(x 1)dx
85/I =
3
1 dx
x 3
86/I =
1
2
1
dx x
87/I =
2
0
sin xdx
88/I =
3
2
ln(sin x) dx cos x
89/I =
2
1
cos(ln x)dx
90*/I =
2
2
ln( x x)dx
91*/I =
3
2
1
dx
x
92/I =
3
1
x dx x
93/I =
3
2
x
dx
x 16
109/I =6
0
x.sin x cos xdx
110*/I =
2 x
2
x e
dx (x 2)
111/I = 2x
0
e sin xdx
112/I =
2
1
x ln(1 )dx
x
99/I =
0
cos x sin xdx
100/I =
2
0
1 sin xdx
101/I =
3
4
sin 2x dx
102/I =
0
1 sin xdx
103/I =
1
2
ln(x x 1) dx
104*/I = 2
0
x sin x dx cos x
105*/I =
1
2 x
1
1
dx
(x 1)(4 1)
106*/I =
4
x
x
dx
107/I =
2
0
x sin xdx
108/I =
2
0
x cos xdx
123/I =
1
3
dx
x 4x 5
124/I =
2
5
dx
x 6x 9
125/I =
1
1
dx
2x 8x 26
126/I =
1
0
2x dx x
127/I =
4
1
dx x (x 1)
(5)113/I =
e
2
e
ln x dx (x 1)
114/I =
1
0
1 x
x.ln dx
1 x
115/I =
2 t
1
ln x
dx I
x
116/I =3
0
sin x.ln(cos x)dx
117/I =e2
cos (ln x)dx
118/I =4
0
1 dx cos x
119*/I =4
3
1 dx cos x
120/I =
1 x
x e dx
121/I =2 sin x2 3
e sin x cos xdx
122/I =2
4
sin 2x dx cos x
137/I =
2
0
sin x
dx (tg x 1) cos x
138/I =
3
2
3
1
dx sin x 9cos x
139/I =
2
cos x dx cos x
128*/I =
0
2
sin 2x dx (2 sin x)
129/I =
1
2
x
dx
(x 1)(x 3x 2)
130/I =
1
4x dx
(x 1)
131/I =
1
4
1
dx
(x 4x 3)
132/I =3
2
sin x dx (sin x 3)
133/I =
3
6
4sin x dx cos x
134/I =
3
2
1
dx cos x.sin x
135/I =3
0
sin x.tgxdx
136/I =
4
1 dx sin 2x
152/I =
1
4x 2x
2x
3e e
dx e
153/I =
4
2
1
dx
x x
154/I = x
e sin xdx
155/I =
4
0
cos x
dx cos x sin x
(6)140/I =
0
1 sin x dx 3cos x
141/I =2
0
cos x
dx sin x cos x
142/I =
4
1
dx x (x 1)
143/I =
1
3
1
dx
x (x 4)
144/I =3
0
sin x dx cos x
145/I =
1
0
x xdx
146/I =
6
4
x
dx
x x
147/I =
0
2
1
dx
x 2x
148/I =
3
2
1
dx
4x x
149/I =
2
2
4x x dx
150/I =
2
2
2x
dx
x 4x 13
151/I =
1
x
1
dx e
167/I = 2x
0
e sin x dx
168/I =
2 x
2
x e
dx (x 2)
169/I =
e
1
(1 x)ln x dx
170/I =
e
x ln x dx
156/I =
1
0
3
dx
x 9 x
157/I =
0
x sin xdx
158/I = 2
0
x cos xdx
159/I =
1
0
cos x dx
160/I =
1
0
sin x dx
161/I =
2
0
x sin x dx
162/I =
2
0
x cos x dx
163/I =
0
x cos x sin x dx
164/I =
x cos x sin x dx
165/I =
4 x
e dx
166/I =4 3x
e sin 4x dx
182/I =2
4
sin 2x dx cos x
183/I =
2
5
dx
x 6x 9
184/I =
2
0
x 3x
dx x
185/I =
4
1 dx
x (x 1)
186/I =
1
ln(1 x) dx
x
(7)171/I =
1 e
2
ln x dx
172/I =
e
1
x(2 ln x)dx
173/I =
2 e
2 e
1
( )dx
ln x
ln x
174/I =
2
(x x)ln x dx
175/I =
2
1
x ln(1 )dx
x
176/I =
2
ln x dx x
177/I =
e
2
e
ln x dx (x 1)
178/I =
1
0
1 x
x ln dx
1 x
179/I =
2
3
cos x.ln(1 cos x)dx
180/2 sin x2 3
e sin x cos x dx
181/I=
4
sin 2x dx sin x
.
197/I =
2
2
x
( ) dx
x
198/I =4
x.tg x dx
199/I =
5
3
( x x )dx
187/I
4
6
1 x dx x
188/I =
1
15
x x dx
189/I =
x
x x
e
dx
e e
190/I=
e
1 e
ln x dx
191/I =2 sin x
(e cos x)cos x dx
192/I =2
0
sin 2x.cos x dx cos x
193/I =2
0
sin 2x sin x dx 3cos x
194/I =4
0
1 2sin x dx sin 2x
195/I =
5 3
2
x 2x
dx
x
196/I =3
2
tgx
dx cos x cos x
212/I =
2
2
x
dx x
213/I =
1
2
x dx x
214/I =
1
2
x
dx
x
215/I =2
0
sin 3x dx cos x
(8)200/I =
4
1
2
dx x
201/I =
2
1
x
dx
x 2 x
202/I =
2
ln(1 x) dx x
203/I =2
0
sin 2x dx cos x
204/I =2 2008
2008 2008
sin x
dx
sin x cos x
205/I =2
0
sin x.ln(1 cos x)dx
206/I = 22
1
x
dx x
207/I =4
2
sin x dx cos x
208/I =2
cos x.cos 4x dx
209/I =
1
2x x
1
dx
e e
210/I =
e
2
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
2x
(1 e ) dx e
216/I =
2 2
2
x
dx x
217/I =
2
4
1 x dx x
218/I =
3
3
x
dx x
219/I =
x ln
x
1 e dx e
220/I =
1
0
x x dx
221/I =
1
x 1dx
222/I =2 3
0
(cos x sin x)dx
223/I =
2
0
x
dx x
224/I =
1
2 2x
(1 x) e dx
225/I =2
2
cos x
dx cos x
226/I =
7
3
x dx 3x
242/I =2
0
sin 2x sin x dx cos3x
243/I =4
2
0
sin 2x
dx sin x 2cos x
244/I =
2
2
x
dx x
(9)229/I =
3
2
0
x (1 x) dx
230/I =
2
sin x.cos x dx cos x
231/I =
1
2
4x dx
x 3x
232*/I =
0
x sin x.cos xdx
233/I =2
0
cos x
dx cos 2x
234/I =
4
1
dx x (x 1)
235/I =2
0
sin 2x(1 sin x) dx
236/I =
2
x dx 3x
237/I =
4
2
1
dx
x x 9
238/I =
0
x sin x cos xdx
239/I =
2
cos x cos x cos xdx
240*/I =
1
2
ln( x a x)dx
241/I =2
x
1 sin x dx (1 cos x)e
255/I =
2
cos x cos x cos xdx
245/I =
2
2
x
dx x
246/I =
2
2 2
1 x dx x
247/I =
2
2
x
dx x
248/I =
2
2
3
1
dx
x x
249/I =
1
5
x (1 x ) dx
250/I =2
0
sin x dx sin x
251/I =2
0
cos x
dx cos 2x
252/I =
4
2
1
dx (1 x)x
253/I =
2
x dx 3x
254*/I =3
4
cos x sin x dx sin 2x
267/I =2
2
sin x dx cos x
268/I =
2
0
sin x dx x
269/I =2
0
sin x cos x(1 cos x) dx
270/I =4 4
0
sin x cos x dx sin x cos x
(10)256/I =
3
4
tg xdx
257*/I =2 x
0
1 sin x
e dx cos x
258/I =
1
2
(1 x ) dx
259/I =4
0
x.tg xdx
260/I=
2
2
1
dx (4 x )
261/I =
2
3
3x
dx
x 2
262*/I =
5
5
1 x
dx x(1 x )
263/I =3
2
cos x dx sin x
264/I =3
6
sin x dx cos x
265/I =6
0
sin x sin x dx cos 2x
265/I =
2
3
1
dx sin x cos x
266/I =
3
6
1
dx x (1 x )
.
281*/I =
2
2
x ln(x x )
dx x
282/I =
4
2
(x 1) ln x dx
271/I =4 4
0
sin x cos x dx sin x cos x
272/I =2
0
sin x cos x cos x dx sin x
273/I =
1 x a
e dx x
274/I =
3
2
x 2x 10x
dx
x 2x
275/I =
3
2
x
dx
(x 1)
276/I =
1
3 dx
x 1
277*/I =
4
6
x
dx
x
278/I =
1
3
x
dx (2x 1)
279/I =
7
2
1
dx x 1
280/I =
3
2
2
1
dx
x x
295/I =
2
2
3
1
dx
x x
296/I =
3
3
x
dx x
297*/I =
2
3
1
dx
x x
298/I =
3
2
x
dx
x x
299/I =
1
2
1
dx
1 x x
(11)283/I =
3
x ln(x 1)dx
284/I =
3
2
3x
dx
x 2x 1
285/I =
1
3
4x
dx
x 2x x
286/I =
1
2
2
1
dx (3 2x) 12x 4x
287/I =
1
0
1
dx
x x
288/I =2
0
cos x
dx cos 2x
289/I =2
4
cos x sin x dx sin 2x
290/I =2 3
0
(cos x sin x)dx
291/I =2
0
cos x sin xdx
292/I =2 4
0
cos 2x(sin x cos x)dx
293/I =2
0
1
dx sin x
294/I =2
0
1
dx cos x
308*/I =
1
2x
1 dx e
309*/I =
2 x
sin x dx
3
300/I =
3
1
dx sin x cos x
301/I =2
0
cos x dx cos x
302/I =2
0
cos x dx cos x
303/I =2
0
sin x dx sin x
304/I =2
0
cos x dx cos x
305/I =
0
1
dx 2cos x sin x
306/I =
2
2
cos x
dx (1 cos x)
307/I =4
tg x dx
321*/I =4
tg x dx
322/I =4
6
cotg x dx
323/I =
4
tg x dx
324*/I =
0
1
dx tgx
(12)310*/I =2
0
sin x
dx cos x sin x
311/I =2
4
0
sin x
dx cos x sin x
312*/I =2
2
tgx
dx ln (cos x)
313*/I =2
0
sin x
dx
cos x sin x
314*/I =
1
x
1
1
dx
(e 1)(x 1)
315*/I =
1
3x
e dx
316*/I =
2
2
x
dx
x 4
317*/I =2
4
0
cos x
dx
cos 3cos x
318*/Tìm x> cho
2 t x
2
t e
dt
(t 2)
319*/I =3
2
tan x
dx cos x cos x
320*/I =
1
2
3x 6x 1dx
325/I =2
0
sin x dx cos x
326/I =
3
2
cos 2x dx cos 2x
327*/I =4
0
t gx
( ) dx
tgx
328*/I =
1
x dx
x 1
329*/I =
3
4
x x dx x
330/I =
x ln
x x
0
e
dx
(e 1) e
331/I =
1 e
2
e
1
dx x cos (ln x 1)
333*/I =4
0
ln(1 tgx)dx
(13)