333 BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC 1/ Cho hàm số : f(x)= x.sinx+x
2
. 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) = mx
3
+(3m+2)x
2
-4x+3 là một nguyên hàm của hàm số:
f(x) = 3x
2
+10x-4.
3/Tìm họ nguyên hàm của hàm số: f(x)= cos
3
x.sin8x.

TÍNH :

4/I =
3
2
4
3tg xdx




2
xdx
8/I =

3
0

(2cos
2
x-3sin
2
x)dx
9 / I =
2
2
sin( x)
4
dx
sin( x)
4








10 / I =


3
sin x sinx
cotgxdx
sin x





14/I =
2
4
0
sin xdx



15/I =

3
4
22
2
cos
2
sin
1


xx

tgx
. 34/I =
1
22
3
1
dx
x 4 x


19/ I =

2
4
4
sin
1


x
dx
20/ I =

4

1 cosx




24/ I =
1
32
0
x 1 x dx


25/I =
1
52
0
x 1 x dx


26/I =
1
0
x
dx
2x 1


27/I =
1
x

x
0
e
dx
e1





31/I =
e
2
1
lnx
dx
x(ln x 1)


32/I =
7
3
3
0
x1
dx
3x 1




2
22
1
x 4 x dx




38/I =
2
23
0
x (x 4) dx


39/I =
2
4
43
3
x4
dx
x



40*/I =
2
2
2




44*/I =
3
0
1
dx
cosx



45/I =
2x
1
x
0
e
dx
e1





46/I =
ln3
x
0
1

e
1
sin(ln x)
dx
x


50/I =
1
3 4 5
0
x (x 1) dx


51/I =
1
23
0
(1 2x)(1 3x 3x ) dx  


52/I =
2
3
1
1
dx
x 1 x



0
e
dx
(e 1)


57/I =
0
2x
3
1
x(e x 1)dx




58/I =
2
6
35
0
1 cos x sin x.cos xdx




59*/I =
23
2
5

.lnxdx
x



63/I =
2
1
0
x
dx
(x 1) x 1
64/I =
2
0
sin x.sin2x.sin3xdx



65/I =
2
44
0
cos2x(sin x cos x)dx





69/I =
9
3
1
x. 1 xdx


70/I =
2
3
0
x1
dx
3x 2




71*/I =
6
0
x
sin dx
2



72*/I =
2





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
.

79/I =



83/I =
2
e
1
lnx
dx
lnx


84/I =
2
2
1
xln(x 1)dx


85/I =
3
2
3
1
dx
x3


86/I =
1
2


90*/I =
2
2
0
ln( 1 x x)dx


91*/I =
3
2
2
1
dx
x1


92/I =
3
8
1
x1
dx
x



93/I =
3
3




96/I =
3
2
4
x 4 dx




97/I =
2
32
1
x 2x x 2 dx

  


98/I =
3
4
4
cos2x 1dx






103/I =
1
3
2
1
ln(x x 1) dx







104*/I =
2
0
xsin x
dx
1 cos x




105*/I =
1
2x
1
1
dx


109/I =
6
2
0
x.sin xcos xdx



110*/I =
2x
1
2
0
xe
dx
(x 2)


111/I =
2x 2
0
e sin xdx




115/I =
2
t
1
ln x
dx I 2
x






116/I =
3
0
sin x.ln(cosx)dx



117/I =
2
e
2
1
cos (lnx)dx



2
sin x 3
0
e .sin xcos xdx



122/I =
2
4
0
sin2x
dx
1 cos x




123/I =
1
2
0
3
dx
x 4x 5


124/I =
2
2

1
1
dx
x (x 1)
128*/I =
0
2
2
sin2x
dx
(2 sin x)




129/I =
1
2
0
x3
dx
(x 1)(x 3x 2)

  


130/I =

3
3
6
4sin x
dx
1 cosx





134/I =
3
2
6
1
dx
cosx.sin x




135/I =
3
0
sin x.tgxdx



136/I =







139/I =
2
2
cosx 1
dx
cosx 2







140/I =
2
0
1 sin x
dx
1 3cosx






144/I =
3
3
0
sin x
dx
cosx



145/I =
1
0
x 1 xdx


146/I =
6
4
x 4 1
. dx
x 2 x 2




147/I =
0
2
1

dx
x 4x 13





151/I =
1
x
0
1
dx
3e


152/I =
1
4x 2x
2
2x
0
3e e
dx
1e




153/I =

1
0
3
dx
x 9 x


157/I =
0
xsinxdx



158/I =
22
0
x cos xdx



159/I =
1
0
cos x dx


160/I =
1
0
sin x dx




165/I =
4
x
1
e dx


166/I =
4
3x
0
e sin4xdx



167/I =
2x 2
0
e sin xdx



168/I =
2x
1
2
0



173/I =
2
e
2
e
11
( )dx
ln x
ln x



174/I =
2
2
1
(x x)ln xdx


175/I =
2
2
1
1
x ln(1 )dx
x




179/I =
2
3
cosx.ln(1 cosx)dx





180/
2
2
sin x 3
0
e sinxcos xdx



181/I=
2
4
0
sin2x
dx
1 sin x








185/I =
4
2
1
1
dx
x (x 1)


186/I =
1
2
0
ln(1 x)
dx
x1




187/I
4
1
6
0
1x
dx


191/I =
2
sin x
0
(e cosx)cosxdx




192/I =
2
0
sin2x.cosx
dx
1 cosx




193/I =
2
0
sin2x sin x
dx
1 3cosx





dx
cosx 1 cos x





197/I =
2
2
1
x1
( ) dx
x2





198/I =
4
2
0
x.tg xdx



199/I =
5
3

x



203/I =
2
0
sin2x
dx
1 cosx




204/I =
2008
2
2008 2008
0
sin x
dx
sin x cos x




205/I =
2
0
sin x.ln(1 cosx)dx

cos x.cos4xdx



209/I =
1
2x x
0
1
dx
ee


210/I =
e
2
1
e
lnx
dx
(x 1)


211/I =
1
0
1
dx
x 1 x



215/I =
2
0
sin3x
dx
cosx 1




216/I =
2
2
2
2
0
x
dx
1x


217/I =
2
2
4
1
1x
dx
1x

0
x 1 x dx


221/I =
1
2
0
x 1dx


222/I =
2
33
0
(cos x sin x)dx




223/I =
2
3
0
x1
dx
x1





.
227/I =
2
6
1 sin 2x cos2x
dx
cosx sin x






228/I =
x2
1
2x
0
(1 e )
dx
1e




229/I =
3
23
0

xsin x.cos xdx



233/I =
2
0
cosx
dx
cos2x 7




234/I =
4
2
1
1
dx
x (x 1)


235/I =
2
23
0
sin2x(1 sin x) dx



2
3
2
cosx cosx cos xdx






240*/I =
1
2
1
ln( x a x)dx




241/I =
2
x
0
1 sinx
dx
(1 cosx)e





x
dx
1x


245/I =
2
3
2
2
0
x
dx
1x


246/I =
2
1
2
2
2
1x
dx
x



247/I =
2

1 sin x




251/I =
2
0
cosx
dx
7 cos2x




252/I =
4
2
1
1
dx
(1 x)x


253/I =
2
3
0
x1
dx



256/I =
3
4
4
tg xdx




257*/I =
2
x
0
1 sin x
e dx
1 cosx





258/I =
1
23
0
(1 x ) dx



5
1
1x
dx
x(1 x )




263/I =
3
2
0
cosx
dx
1 sin x




264/I =
2
3
6
0
sin x
dx
cos x



.

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 xcosx(1 cosx) dx

2
0
sin xcosx cosx
dx
sin x 2





273/I =
1
1
x
3
a
e
dx
x


274/I =
32
1
2
0
x 2x 10x 1
dx
x 2x 9
  





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

284/I =
3
2
2
1
3x
dx
x 2x 1


285/I =
1
32
0
4x 1
dx
x 2x x 2

  


286/I =
1
2
2
1
2
1
dx
(3 2x) 5 12x 4x





290/I =
2
33
0
(cos x sin x)dx




291/I =
2
54
0
cos xsin xdx



292/I =
2
44
0
cos2x(sin x cos x)dx






296/I =
3
7
3
2
0
x
dx
1x


297*/I =
2
3
1
1
dx
x 1 x


298/I =
3
1
2
0
x
dx
x 1 x


cosx 1




302/I =
2
0
cosx
dx
2 cosx




303/I =
2
0
sin x
dx
sin x 2




304/I =
3
2
0
cos x

4
3
0
tg x dx


.
308*/I =
1
2x
1
1
dx
3e




309*/I =
2
x
sin x
dx
31




1 ln (cosx)




313*/I =
2
0
sin x
dx
cosx sin x




314*/I =
1
x2
1
1
dx
(e 1)(x 1)




315*/I =
1
3x 1
0

0
te
dt 1
(t 2)




319*/I =
3
2
4
tan x
dx
cosx cos x 1





320*/I =
1
2
0
3x 6x 1dx  
321*/I =
4





325/I =
5
2
0
sin x
dx
cosx 1




326/I =
3
2
6
cos2x
dx
1 cos 2x





327*/I =
4
2


330/I =
x
ln3
xx
0
e
dx
(e 1) e 1


331/I =
1
4
e
2
1
e
1
dx
xcos (ln x 1)





333*/I =
4
0
ln(1 tgx)dx