LT ĐH
TÍCH
PHÂN
1/ ∫cos xdx
2/ dx2
∫
+ .
3/I=∫cos x.sin 8x3 dx
4/I =
π
π
4
3tg x dx
∫
5/I =
π
π
6
(2cotg x 5) dx
6/I =
π
2
0
1 cos x
dx
1 cos x
∫ −
+
7/ I =
π
2
0 ∫ sin2 x.cos2xdx
8/I =
π
3
0
∫ (2cos2 x-3sin2 x)dx
9 / I =
π
2
π
2
π
sin( x)
π
sin( x)
4
∫
−
−
+
10 / I =
π
3
π
6
∫
− (tgx-cotgx)2 dx
11/ I =
π
0 ∫cos x dx
12 / I =
π
0sin x dx
13*/ I =
π
3
2
π
3
sin x sin xcot gx dx
sin x
14/I =
π
0 ∫sin x dx
15/I =
π
3
4
1
sin cos
16/I =
π
4
π
6
∫ cotg2x dx
17/I =
π
2
2 sin x
π
4
e sin 2x dx
18/ I =
π
tgx 2
4
2 0
e
cos x
+
∫
19/ I =
π
2
4
π
4
1
sin x
∫ dx20/ I =
π
4
6
0
1
cos x
∫ dx
21/I =
π
0 ∫cos 2x(sin x cos x)dx+ 22/ I =
π
0 ∫cos xdx 23/ I =
π 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
∫
+
28/I =2 x
1
1 dx
1 e
∫ −
−
29/I =2 x2x
0
e dx
∫
+
30/I =1 xx
0
e dx
−
∫ − +
31/I =e1 2
ln x dx x(ln x 1)
∫
+
32/I =
7 3 3
x 1 dx 3x 1
∫ + +
33/I =2 3 2
0(x 3) x 6x 8 dx
34/I = 1 2 2
3
1 dx
∫
−
35/I =42 1 2dx
x 16 x
∫
−
36*/I = 6 2
2 3
1 dx
∫
−
37/I = 2 2 2
1x 4 x dx
∫
38/I =2 2 3
0x (x 4) dx
39/I =
2 4
4 3 3
x 4dx x
40*/I = 2 22
2
dx
−
∫
−
+ +
41/I =ln 2 x
42/I =1
0
1 dx
3 2x
∫
−
43/I =
π
0 ∫sin xdx
44*/I =
π 3 0
1 dx cos x
∫
45/I =1 x2x
0
e dx
−
∫ − +
46/I =ln 30 x1 dx
∫
+
47/I =
π 4 2 π 6
sin x cot gx
∫
48/I =e 3 2
1
ln x 2 ln xdx x
49/I =e
1
sin(ln x) dx x
∫
50/I =1 3 4 5
0 ∫x (x −1) dx
0 ∫(1 2x)(1 3x 3x ) dx+ + + 52/I =21 1 3dx
x 1 x
∫
+
53/I =
π
π 6
tg x cot g x 2dx
54/I =1 2 3
0 ∫ (1 x ) dx−
55*/I =1 2x
0
1 dx
∫
+
56/I =
x
ln 3
0
e dx (e 1)
∫
+
57/I = 0 2x 3
1x(e x 1)dx
∫
58/I =
π
0 ∫ 1 cos x sin x.cos xdx−
59*/I =2 3 2
5
1 dx
∫
+
60/I =
π 4 0
1 cos 2x
∫
+
61/I =ln 5 x2x
ln 2
∫
−
62/I =e 2
1
x 1.ln xdx x
∫ +
63/I =1 2
0
x dx (x 1) x 1
∫
+ +
64/I =
π 2
0 ∫sin x.sin 2x.sin 3xdx
65/I =
π
0 ∫cos 2x(sin x cos x)dx+
66*/I =
π
0 ∫( cos x− sin x )dx
67/I =3 87 4
2
x dx
∫
+ −
68*/I =
π 2 0
4cos x 3sin x 1dx 4sin x 3cos x 5
+ +
69/I =9 3
1 ∫x 1 xdx−
70/I =23x 1 dx
3x 2
∫ + +
71*/I =π 6 0
x sin dx 2
∫
72*/I =2
0
x dx
∫
+ + −
73/I = 3 3 2
0 ∫ x 1 x dx+
74**/I =10 2
ln(1 x) dx
∫ + +
75/I =
π 2 0
sin x dx sin x cos x
∫
+
76/I =eπ
1 cos(ln x)dx
∫
77*/I =2 2
0 ∫ 4 x dx+
78/I =2
1
x dx
∫
+ −
79/I =e
1
1 3ln x ln xdx x
∫ +
80/I =3 2
81/I =e 2
1 ∫(ln x) dx
82/I =e2
e
ln xdx x
∫
83/I =e2
1
ln x dx
ln x
∫
84/I =2 2 1
x ln(x 1)dx
85/I = 3 2 3
1 dx
∫
+
86/I =10 1 2dx
4 x
∫
−
87/I =
2 4
0 ∫ sin xdx
88/I =
π 3 2 π 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
∫
−
92/I = 3
1
x 1dx x
∫ +
93/I =3 2 3
1
x 16
∫
−
94/I =
π 6
2 0
cos x
dx
6 5sin x sin x
∫
− +
95*/I =e2 2
e
ln x
ln x
96/I = 3 2
∫
− −
97/I =2 3 2
1x 2x x 2 dx
∫
98/I =
3π 4 π 4
cos 2x 1dx
99/I =π
0 ∫cos x sin xdx
100/I =2π
0 ∫ 1 sin xdx+
101/I =
3π 4 π 4
sin 2x dx
∫
102/I =π
0 ∫ 1 sin xdx−
1 ln(x x 1) dx
∫
−
+ +
104*/I =π 2
0
x sin x dx
1 cos x
∫
+
105*/I =11 2 x
1 dx (x 1)(4 1)
∫
106*/I =1 4x
1
x dx
1 2
∫
− +
107/I =
2 4
0 ∫ x sin xdx
108/I =
2 4
0 ∫ x cos xdx
109/I =
π
0 ∫x.sin x cos xdx
110*/I =1 2 x2
0
x e dx (x 2)
∫
+
111/I =π 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 =t 2
1
ln x
x
∫ ⇒ <
÷
116/I =
π 3 0 sin x.ln(cos x)dx
∫
117/I =
π 2
1 ∫ cos (ln x)dx
118/I =
π 4 0
1 dx cos x
∫
119*/I =
π 4 3 0
1 dx cos x
∫
120/I =1 3 x2
0 ∫x e dx
121/I =
π 2
0 ∫e sin x cos xdx
122/I =
π 2 4 0
sin 2x dx
1 cos x
∫
+
123/I =10 2
∫
− −
124/I =21 2
∫
− +
125/I =15 2
∫
126/I =1
0
2x 9dx
x 3
∫ + +
127/I =41 2
x (x 1)
∫
+
128*/I =
0
2 π
2
sin 2x dx (2 sin x)
∫
− +
129/I =10 2
(x 1)(x 3x 2)
+ + +
130/I =1 3 0
4x dx (x 1)
∫
+
131/I =10 4 2
∫
+ +
132/I =
π 3 3 2 0
sin x dx (sin x 3)
∫
+
133/I =
π 3 3 π 6
4sin x dx
1 cos x
∫
−
134/I =
π 3 2 π 6
1 dx cos x.sin x
∫
135/I =
π 3
0 ∫sin x.tgxdx
136/I =
π 3 π 4
1 dx sin 2x
∫
137/I =
π
3 4
0
(tg x 1) cos x
∫
+
138/I =
π 3
π 3
sin x 9 cos x
∫
1
Trang 2139/I =
π
2
π
2
cos x 1dx
cos x 2
∫
−
−
+
140/I =
π
2
0
1 sin x dx
1 3cos x
∫ +
+
141/I =
π
2
0
cos x
dx sin x cos x 1
∫
+ +
142/I = 41 2
1
dx
x (x 1)
∫
+
∫
144/I =
π
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 = 01 2 1 dx
∫
148/I =31 1 2dx
4x x
∫
−
149/I = 2 2
∫
150/I = 22 22x 5 dx
∫
−
−
+ +
151/I =10 1 xdx
3 e
∫
+
152/I =
1
2
2x
0
dx
1 e
+
7
1
dx
x 9 x
∫
+
154/I =
π
0 ∫e sin xdx
155/I =
π
4
2
0
cos x
dx cos x sin x
∫
+
156/I =1
0
3
dx
∫
+ −
157/I = π
0 ∫x sin xdx
158/I =π 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
π
4
0 ∫ x cos x dx
163/I =π 2
0 ∫x cos x sin x dx
164/I =
π
0 ∫x cos x sin x dx
165/I =4 x
166/I =
π
4 3x
0 ∫e sin 4x dx
167/I =π 2x 2
0 ∫e sin x dx
168/I =1 2 x2
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
1 ∫ln x dx
172/I =e
1 x(2 ln x) dx
∫ −
173/I =e2 2
e
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
−
179/I =
π 2 π 3
cos x.ln(1 cos x) dx
180/
π 2
0
e sin x cos x dx
∫
181/I=
π 2 4 0
sin 2x dx
1 sin x
∫
+
182/I =
π 2 4 0
sin 2x dx
1 cos x
∫
+
183/I =2 2 1
∫
− +
184/I =1 2
0
x 3x 2dx
x 3
∫ + + +
185/I =41 2
x (x 1)
∫
+
186/I =1 2
0
ln(1 x) dx
∫ + +
187/I1 64
0
1 x dx
1 x
∫ + +
188/I =1 15 8
0 ∫x 1 x dx+
189/I =1 x x x
0
∫
−
+
190/I=
e 1 e
ln x dx
∫
191/I =
π
0 ∫(e +cos x) cos x dx
192/I =
π 2 0
sin 2x.cos x
dx
1 cos x
∫
+
193/I =
π 2 0
sin 2x sin xdx
1 3cos x
+
194/I =
π 2 4 0
1 2sin x
dx
1 sin 2x
∫ − +
195/I = 3 5 2 3
0
dx
∫ + +
196/I =
π 3
2 π
4
cos x 1 cos x
∫
+
197/I =2 2
1
x 1
x 2
∫
−
− +
198/I =
π
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
∫
+ + −
202/I =2 2
1
ln(1 x) dx x
∫ +
203/I =
π 2 0
sin 2x dx
1 cos x
∫
+
204/I =
π 2008 2
0
dx
∫
+
205/I =
π 2 0 sin x.ln(1 cos x) dx
206/I = 3 22
1
dx x
207/I =
π 3 4 2 0
sin xdx cos x
∫
208/I =
π
0 ∫cos x.cos 4x dx
209/I =1 2x x
0
1 dx
∫
+
210/I =
e 2 1 e
ln x dx (x 1)
∫
+
211/I =1
0
∫
+ +
212/I =1 22
0
4 x
∫
−
213/I =1 2 0
x dx
4 x
∫
−
214/I =
1 4 2 2 0
x dx
∫
−
215/I =
π 2 0
sin 3x dx cos x 1
∫
+
216/I =
2 2 2 2 0
x dx
1 x
∫
−
217/I =2 24
1
1 x dx
1 x
∫ − +
218/I = 73 3 2
0
x dx
1 x
∫
+
219/I =ln 2 xx
0
1 e dx
1 e
∫ − +
220/I =1
0 ∫x 1 x dx−
221/I =1 2
222/I =
π
0 (cos x sin x) dx
223/I =3 2
0
x 1dx
x 1
∫ + +
224/I =1 2 2x 0
(1 x) e dx
∫ +
225/I =
π 2 2 0
cos x dx cos x 1
∫
+
226/I =
7 3 3
x 1 dx 3x 1
∫ + +
227/I =
π 2 π 6
1 sin 2x cos 2x
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 =
π 3 2 2 0
sin x.cos x
dx cos x 1
∫
+
231/I =
1 2 2 0
4x 1 dx
− +
0
x sin x.cos xdx
∫
233/I =
π 2 0
cos x dx cos 2x 7
∫
+
234/I =41 2
1 dx
x (x 1)
∫
+
235/I =
π
0 ∫ sin 2x(1 sin x) dx+
236/I =23x 1 dx
3x 2
∫ + +
237/I = 4 2
7
1 dx
∫
+
238/I =π 3 4
0 ∫x sin x cos xdx
239/I =
π
π 2
cos x cos x cos xdx
∫
−
−
240*/I =1 2
1ln( x a x)dx
∫
241/I =
π 2
x 0
1 sin x dx (1 cos x)e
∫ − +
242/I =
π 2 0
sin 2x sin x
dx cos3x 1
+
243/I =
π 4
0
sin 2x dx sin x 2 cos x
∫
+
244/I =
2 3 2 2 0
x dx
1 x
∫
−
245/I =
2 3 2 2 0
1 x
∫
−
246/I =
2 1 2 2 2
1 x dx x
∫ −
247/I =1 2 2
0
4 x
∫
−
248/I =
2 2 2 3
1 dx
∫
−
249/I =1 5 3 6
0 ∫x (1 x ) dx−
250/I =
π 2 0
sin x dx
1 sin x
∫
+
251/I =
π 2 0
cos x dx
7 cos 2x
∫
+
252/I =41 2
1 dx (1 x)x
∫
+
253/I =23x 1 dx
3x 2
∫ + +
254*/I =
π 3 π 4
cos x sin xdx
3 sin 2x
+
255/I =
π
π 2
cos x cos x cos xdx
∫
−
−
256/I =
π
π 4
tg xdx
∫
257*/I =
π
0
1 sin x
e dx
1 cos x
∫ + +
258/I =1 2 3
0 ∫ (1 x ) dx−
259/I =
π
0 ∫x.tg xdx
260/I=20 2 2
(4 x )
∫
+
261/I = 1 32
0
3x dx
∫
+
262*/I = 2 55
1
1 x dx x(1 x )
∫ − +
263/I =
π 3 2 0
cos x dx
1 sin x
∫
−
264/I =
π 2 3 6 0
sin xdx cos x
∫
265/I =
π
3 6
0
sin x sin x
dx cos 2x
266/I = 13 6 2
x (1 x )
∫
+
267/I =
π 2 2 0
sin x dx cos x 3
∫
+
268/I = 2
0
sin xdx x
∫
269/I =
π
0 ∫sin x cos x(1 cos x) dx+
270/I =
π
4 0
sin x cos xdx sin x cos x 1
+ +
271/I =
π
4 0
sin x cos x
dx sin x cos x 1
+ +
272/I =
π 2 0
sin x cos x cos xdx sin x 2
+
273/I =
1 x 1 3 a
e dx x
∫
274/I =1 3 2 2
0
dx
+ +
275/I =1 23 3
0
x dx (x 1)
∫
+
276/I =10 3
3 dx
∫
+
277*/I =1 46
0
x 1dx
∫ + +
278/I =10 3
(2x 1)
∫
+
279/I =7
2
2 x 1
∫
+ +
2
Trang 3280/I =
3
2
2
1
2
x 1 x
∫
−
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
3x
dx
∫
+ +
285/I =1 3 2
0
4x 1
dx
+ + +
286/I =
1
2
2 1
2
1
dx (3 2x) 5 12x 4x
∫
287/I =1
0
∫
+ +
288/I =
π
2
0
cos x
dx
2 cos 2x
∫
+
289/I =
π
2
π
4
cos x sin xdx
3 sin 2x
+
290/I =
π
0 ∫(cos x sin x)dx+
291/I =
π
0 ∫cos x sin xdx
292/I =
π
0 ∫cos 2x(sin x cos x)dx+
293/I =
π
2
0
2 sin x
∫
+
294/I =
π
2
0
1
dx
2 cos x
∫
−
295/I =
2
2
2
3
∫
−
296/I = 73 3 2
0
1 x
∫
+
297*/I =12 1 3dx
x 1 x
∫
+
298/I =1 3 2
0
∫
+ +
299/I =11 1 2dx
∫
− + + +
300/I =
π
3
4
π
6
1
dx sin x cos x
∫
301/I =
π
2
0
cos x
dx
cos x 1
∫
+
302/I =
π
2
0
cos x dx
2 cos x
∫
−
303/I =
π
2
0
sin x
dx
sin x 2
∫
+
304/I =
π
3
2
0
cos x dx
cos x 1
∫
+
305/I =
π
2
0
1
dx
2 cos x sin x 3
∫
+ +
306/I = 2π 2
3
cos x dx (1 cos x)
∫
−
307/I =
π
0
tg x dx
∫
308*/I =1 2x
1
1 dx
3 e
∫
− +
309*/I = π x2
π
sin xdx
∫
− +
310*/I =
π 2 0
sin x dx cos x sin x
∫
+
311/I =
π 4 2
0
cos x sin x
∫
+
312*/I =
π 2 2 0
tgx dx
1 ln (cos x)
∫
−
313*/I =
π 2 0
sin x dx cos x sin x
∫
+
314*/I =11 x 2
(e 1)(x 1)
∫
315*/I =1 3x 1
316*/I =1 22
0
x dx
∫
+
317*/I =
π
3 2
0
cos 3cos x 3
∫
− +
318*/Tìm x> 0 sao cho
2 t x 2 0
t e
dt 1 (t 2)
+
319*/I =
π 3
2 π
4
tan x
dx cos x cos x 1
∫
+
320*/I =1 2
0 ∫ −3x +6x 1dx+
321*/I =
π
0 ∫tg x dx
322/I =
π
π 6
cotg x dx
∫
323/I =
π
π 4
tg x dx
∫
324*/I =
π 4 0
1 dx
2 tgx
∫
+
325/I =
π 5 2 0
sin x dx cos x 1
∫
+
326/I =
π 3 2 π 6
cos 2x dx
1 cos 2x
∫
−
327*/I =
π
0
t gx 1
tgx 1
+
328*/I =
1 3 1 2
x dx
∫
+
329*/I =23 4 3
1
x x dx x
∫ −
330/I =
x
ln 3
0
∫
+ −
331/I =
π 1 4 e 2 1 e
x cos (ln x 1)
−
∫
+
332/I =2π
3
sin x 1 cos x
∫
+
333*/I =
π 4 0 ln(1 tgx)dx
∫ +
3