333 Bài toán tích phân
Trang 1Tröông Vaên Höng 12A1 K30 HÑB General 4 1
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) = mx3+(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)= cos3x.sin8x
TÍNH :
4/I = 3 2
4
3tg x dx
6
(2cotg x 5)dx
6/I = 2
0
1 cos x dx
1 cos x
7/ I =2
0
sin2x.cos2xdx
8/I = 3
0
(2cos2x-3sin2x)dx
9 / I = 2
2
s i n (x )
s i n (x )
4
10 / I =
3
6
(tgx-cotgx)2 dx
11/ I = 4 4
0cos x dx
12 / I = 2 3
0 sin x dx
13*/ I = 2 3 3
3
sin x sin x cotgxdx sin x
14/I = 2 4
0sin x dx
15/I = 3
4
2 2
2
cos 2 sin
1
x x dx
16/I = 4
6
cotg2x dx
17/I = 2 sin x2
4
e sin 2x dx
18/ I = 4
2
cos
x
etgx
.
Trang 2Tröông Vaên Höng 12A1 K30 HÑB General 4 2
19/ I = 2
4
4
sin
1
20/ I = 4
0 cos6 1
x dx
21/I = cos2x(si n4x cos4 x)dx
2
0
22/ I = 2 3
0cos xdx
23/ I = 2 3
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
2x 1
27/I =1 x
0
1 dx
e 4
28/I =2 x
1 e
29/I =2 x2x
0
e 1
30/I =1 x x
0
31/I =e 2
1
x(ln x 1)
32/I =
7
3
3
0
x 1 dx
3x 1
34/I = 1
3
x 4 x
35/I =4
2 2
x 16 x
36*/I = 6
2
2 3
x x 9
37/I = 2 2 2
1
x 4 x dx
0
x (x 4)dx
39/I = 4 2
4 3 3
x
40*/I = 2 2
2
x x 1
41/I =ln 2 x
0
e 1dx
42/I =1
0
3 2x
43/I =2 5
0 sin xdx
44*/I =3
0
1 dx cos x
45/I =1 x2x
0
46/I =ln 3
x 0
e 1
47/I =4 2
6
sin x cot gx
1ln x 2 ln xdx
x
Trang 3Tröông Vaên Höng 12A1 K30 HÑB General 4 3
33/I =2 3 2
0
(x 3)x 6x 8 dx
.
49/I =e
1sin(ln x)dx
x
50/I =1 3 4 5
0
x (x 1)dx
0
(1 2x)(1 3x 3x )dx
52/I =2
3 1
x 1 x
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 =ln 3 x
0
(e 1)
57/I = 0 2x 3
1
0
1 cos x sin x.cos xdx
59*/I =2 3
2 5
x x 4
60/I =4
0
1 cos2x
61/I =ln 5 2x
x
ln 2
e 1
.
64/I =2
0sin x.sin 2x.sin3xdx
0cos2x(sin x cos x)dx
66*/I =2 3 3
0(cos x sin x)dx
67/I =3 8 7 4
2
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
3x 2
71*/I = 6
0
x
2
72*/I =2
0
2 x 2 x
73/I = 3 3 2
0
x 1 x dx
74**/I =1 2
0
ln(1 x)dx
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
Trang 4Tröông Vaên Höng 12A1 K30 HÑB General 4 4
62/I =e 2
1x 1.lnxdx
x
63/I =1 2
0
(x 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 =
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
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
0
ln(1 x x)dx
91*/I = 3
2 2
x 1
78/I =2
1
1 x 1
.
0
6 5sin x sin x
95*/I =
2
e 2 e
()dx
ln x
ln x
96/I = 3 2
4
97/I = 2 3 2
1
98/I =
3 4 4
cos2x 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
1
0 xsin x dx
1 cos x
105*/I = 1 2 x
1
106*/I = 1 4x
1
x dx
1 2
Trang 5Tröông Vaên Höng 12A1 K30 HÑB General 4 5
92/I =8 3
x
93/I =3 2 3
1
x 16
.
0x.sin x cos xdx
110*/I =1 2 x 2
(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
1 x
115/I =
2 t
x
116/I =3
0sin x.ln(cos x)dx
117/I =
2
e
2 1
cos (ln x)dx
118/I =4
0
1 dx
cos x
119*/I =4 3
0
1 dx cos x
107/I =
2
4 0 xsin xdx
108/I =
2
4
0 x cos xdx
123/I =1 2
0
x 4x 5
124/I =2 2
1
x 6x 9
125/I = 1 2
5
126/I =1
0 2x 9 dx
x 3
127/I =4 2
1
x (x 1)
2
sin 2x dx (2 sin x)
0
130/I =1 3
(x 1)
131/I =1 4 2
0
(x 4x 3)
132/I =3 2 3
0
sin x dx (sin x 3)
133/I =3 3
6
4sin x dx
1 cos x
Trang 6Tröông Vaên Höng 12A1 K30 HÑB General 4 6
120/I =1 3 x2
0
x e dx
121/I =2 sin x2 3
0
e sin x cos xdx
122/I =2 4
0
sin 2x dx
1 cos x
137/I = 4 2 32 5
0
(tg x 1).cos x
3
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
sin x cos x 1
142/I = 4 2
1
x (x 1)
143/I = 1
3 3
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
6
cos x.sin x
135/I =3
0 sin x.tgxdx
136/I = 3
4
1 dx sin 2x
.
152/I =
1
2
2x 0
1 e
153/I = 4
2 7
x 9 x
154/I = 2 x 2
0e sin xdx
155/I = 2 4 4 4
0
cos x sin x
156/I =1
0
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 xsin x dx
Trang 7Tröông Vaên Höng 12A1 K30 HÑB General 4 7
148/I =3
2 1
4x x
1
150/I = 2
2 2
151/I =1
x 0
3 e
167/I = 2x 2
0
e sin x dx
168/I =1 2 x 2
(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
1ln x dx
172/I =e
1
x(2 ln x)dx
173/I =
2
e
2 e
()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)
178/I =
1
2
0
1 x
1 x
162/I =
2
4 0
x cos x dx
0
x cos xsin x dx
164/I = 6 2
0x cos xsin 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
x 6x 9
184/I =1 2
0
x 3
185/I =4 2
1
x (x 1)
186/I =1 2
0ln(1 x)dx
187/I1 46
0
1 x dx
1 x
188/I =1 15 8
0
x 1 x dx
189/I =1 x
0
e e
190/I= e
1 e
ln x dx
191/I =2 sin x
0(e cos x)cos x dx
Trang 8Tröông Vaên Höng 12A1 K30 HÑB General 4 8
179/I =2
3
cos x.ln(1 cos x)dx
0
e sin x cos x dx
0
sin 2x dx
1 sin x
.
1
x 1
()dx
x 2
198/I =4 2
0x.tg x dx
199/I = 5
3
(x 2 x 2 )dx
200/I = 4
1
x 5 4
201/I =2
1
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 =2 2008 2008 2008
0
205/I =2
0
sin x.ln(1 cos x)dx
206/I = 3 22
1
x 1 dx x
192/I =2
0sin 2x.cos x dx
1 cos x
193/I =2
0sin 2x sin x dx
1 3cos x
01 2sin x dx
1 sin 2x
195/I = 3 5 3
2 0
x 1
196/I =3
2 4
cos x 1 cos x
212/I =1 2 2
0
4 x
213/I =1 2
4 x
214/I =
1 4 2 2
x 1
215/I =2
0 sin3x dx cos x 1
216/I =
2 2 2
2 0
1 x
217/I =2 24
1
1 x dx
1 x
218/I = 7 3
0
1 x
219/I =ln 2 xx
0 1 e dx
1 e
220/I =1
0
x 1 x dx
Trang 9Tröông Vaên Höng 12A1 K30 HÑB General 4 9
207/I =4 32
0 sin x dx
cos x
208/I =2 2
0cos x.cos4x dx
209/I =1 2x x
0
e e
210/I =e 2
1
e
ln x dx
(x 1)
211/I =1
0
x 1 x
227/I =2
6
1 sin 2x cos2x dx
cos x sin x
228/I =1 x 22x
0
(1 e ) dx
1 e
229/I =3 2 3
0
x (1 x)dx
230/I = 2 2 3
0sin x.cos x dx
cos x 1
231/I =
1
2
2
0
4x 1
dx
0
xsin x.cos xdx
233/I =2
0
cos x dx cos2x 7
234/I =4 2
1
x (x 1)
0
sin 2x(1 sin x)dx
221/I =1 2
0
x 1dx
0 (cos x sin x)dx
223/I =3 2
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
.
242/I =2
0
sin 2x sin x dx cos3x 1
0
sin x 2cos x
244/I =
2 3 2
2 0
1 x
245/I =
2 3 2
2 0
1 x
246/I = 1 2 2
2 2
1 x dx x
247/I =1 2
2 0
4 x
248/I = 2
2 2
3
x x 1
Trang 10Tröông Vaên Höng 12A1 K30 HÑB General 4 10
236/I =2 3
0
x 1 dx
3x 2
237/I = 4
2 7
x x 9
0
xsin x cos xdx
2
cos x cos x cos xdx
240*/I = 1 2
1
0
1 sin x dx
(1 cos x)e
2
cos x cos x cos xdx
256/I =3 4
4
tg xdx
01 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
(4 x )
261/I = 1 2
3 0
x 2
262*/I = 2 55
1
1 x dx x(1 x )
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 cos2x
1
(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
.
267/I =2 2
0
sin x dx cos x 3
268/I =
2
0
sin x dx x
0 sin x cos x(1 cos x)dx
0
sin x cos x dx sin x cos x 1
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
Trang 11Tröông Vaên Höng 12A1 K30 HÑB General 4 11
263/I =3 2
0 cos x dx
1 sin x
264/I =3 26
0 sin x dx
cos x
0sin x sin x dx
cos2x
265/I =2
3
sin x 1 cos x
266/I = 3 6 2
1
x (1 x )
.
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 =2 2 3
1
x 2x 1
285/I =1 3 2
0
286/I =
1
2
2 1
2
(3 2x)5 12x 4x
287/I =1
0
x 1 x
288/I =2
0
cos x dx
2 cos2x
273/I =
1
1 x 3
x
274/I =1 3 2 2
0
275/I =1 2 3 3
0
(x 1)
276/I =1 3
0
3 dx
x 1
277*/I =1 46
0
x 1dx
x 1
0
(2x 1)
279/I =7
2
2 x 1
280/I =
3 2
2 1
2
x 1 x
.
295/I = 2
2 2
3
x x 1
296/I = 7 3
0
1 x
297*/I =2
3 1
x 1 x
298/I =1 3
2 0
x 1 x
299/I =1
2 1
Trang 12Tröông Vaên Höng 12A1 K30 HÑB General 4 12
289/I =2
4
cos x sin x dx
3 sin 2x
0(cos x sin x)dx
291/I =2 5 4
0cos xsin xdx
0cos2x(sin x cos x)dx
293/I =2
0
2 sin x
294/I =2
0
2 cos x
308*/I = 1 2x
1
1 dx
3 e
309*/I = sin x dxx 2
3 1
310*/I =2
0
sin x dx cos x sin x
311/I =2 4 4 4
0
cos x sin x
312*/I =2
2 0
1 ln (cos x)
313*/I =2
0
cos x sin x
314*/I = 1 x 2
1
300/I =3 4
6
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 =2 3
0
cos x dx cos x 1
305/I = 2
0
2cos x sin x 3
3
cos x dx (1 cos x)
307/I =4 3
0
tg x dx
321*/I =4 5
0tg x dx
322/I =4 3
6
cotg x dx
323/I = 3 4
4
tg x dx
Trang 13Tröông Vaên Höng 12A1 K30 HÑB General 4 13
.
315*/I =1 3x 1
0
e dx
316*/I =1 2
2 0
x 4
317*/I =2 4 3 2
0
cos 3cos x 3
318*/Tìm x> 0 sao cho x 2 t 2
(t 2)
319*/I =3
2 4
cos x cos x 1
320*/I =1 2
0
324*/I = 4
2 tgx
325/I =2 5
0 sin x dx cos x 1
326/I =3 2
6
cos2x dx
1 cos 2x
0
t gx 1 ()dx tgx 1
328*/I =1 3
1 2
x dx
x 1
329*/I =2 3 4 3
x
330/I =ln 3 x
0
(e 1)e 1
331/I =
1 4
e
2 1
e
x cos (ln x 1)
333*/I =4
0ln(1 tgx)dx