Tài liệu 333 BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC 2010 ppt

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




5/I =
4
2
6
(2cotg x 5)dx





6/I =
2
0
1 cosx
dx
1 cosx





7/ I =

2
0

sin
2
x.cos

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
6


(tgx-cotgx)
2
dx
11/ I =
4
4
0
cos xdx





12 / I =
2
3
0
sin xdx



13*/ I =
3
3
2

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

dx

16/I =

4
6


cotg2x dx
17/I =
2
2
sin x
4
e sin2xdx




18/ I =


4
0
2
2
cos

x
e

tgx



.


34/I =
1
22
3
1
dx
x 4 x


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

0
6
cos
1

x
dx
21/I =
dxxxnsix )cos(2cos
44
2
0




22/ I =
2
3
0
cos xdx



23/ I =
3
2
0
4sin x
dx

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

0
1
dx
e4


28/I =
2
x
1
1
dx
1e




29/I =
2x
2
x
0
e
dx
e1


30/I =
x
1

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




33/I =
2
3
2
0
(x 3) x 6x 8dx  


.

35/I =
4
2
2
1
dx
x 16 x


36*/I =
6
2
23
1
dx
x x 9


37/I =

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

2
x1
dx
x x 1






41/I =
ln2
x
0
e 1dx


42/I =
1
0
1
dx
3 2x


43/I =
2
5
0
sin xdx




44*/I =
3
0
1
dx
cosx



45/I =
2x
1
x
0
e
dx
e1





46/I =
ln3
x
0
1

dx
e1


47/I =
4
2
6
1
dx
sin x cotgx




48/I =
3
2
e
1
lnx 2 ln x
dx
x



.


49/I =

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


53/I =
3
22
6
tg x cotg x 2dx





54/I =
1
23
0
(1 x ) dx


55*/I =
1
2x
0
1
dx
e3


56/I =
x
ln3
x3

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

1
dx
x x 4


60/I =
4
0
x
dx
1 cos2x




61/I =
2x
ln5
x
ln2
e
dx
e1


62/I =
2
e
1
x1

.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




66*/I =
2
33
0
( cosx sin x)dx




67/I =
7
3
84
2
x
dx
1 x 2x


68*/I =
2
0
4cosx 3sinx 1
dx
4sinx 3cosx 5





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

0
x
dx
2 x 2 x  


73/I =
3
32
0
x . 1 x dx


74**/I =
1
2
0
ln(1 x)
dx
x1




75/I =
2
0
sin x
dx
sin x cosx





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 =

e
1
1 3lnx 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
lnx
dx
x



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

0
1
dx
4x


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


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

2
1
x
dx
x 16



.

94/I =
6
2
0
cosx
dx
6 5sinx sin x




95*/I =
2
e
2
e
11
( )dx
ln x
ln x




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





99/I =
0
cosx sin xdx



100/I =
2
0
1 sinxdx




101/I =
3
4
4
sin 2x dx




102/I =
0
1 sinxdx




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

(x 1)(4 1)




106*/I =
4
1
x
1
x
dx
12




107/I =
2
4
0
xsin xdx



108/I =
2
4
0
xcos xdx





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



112/I =
2
2
1
1
x ln(1 )dx
x




113/I =
e
2
1
e
lnx
dx
(x 1)


114/I =
1
2
0
1x
x.ln dx
1x





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



118/I =
4
0
1
dx
cosx



119*/I =
4
3
0
1
dx
cos x



120/I =
2
1
3x
0
x e dx


121/I =
2

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
5
dx
x 6x 9


125/I =
1
2
5
1
dx
2x 8x 26




126/I =
1
0
2x 9
dx
x3




127/I =
4
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 =

1
3
0
4x
dx
(x 1)


131/I =
1
42
0
1
dx
(x 4x 3)


132/I =
3
3
2
0
sin x
dx
(sin x 3)




133/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 =

3
4
1
dx
sin 2x





.
137/I =
3
4
2 2 5
0
sin x
dx
(tg x 1) .cos x




138/I =
3
22
3
1
dx
sin x 9cos x







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

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

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

142/I =
4
2
1
1
dx
x (x 1)


143/I =
1
3
3
1
dx
x 4 (x 4)

  


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

1
dx
x 2x 9




148/I =
3
2
1
1
dx
4x x


149/I =
2
2
1
4x x 5dx




150/I =
2
2
2
2x 5

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 =

4
2
7
1
dx
x 9 x


154/I =
2
x2
0
e sin xdx



155/I =
4
2
44
0
cos x
dx
cos x sin x





156/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



161/I =
2
4
0
xsin x dx



162/I =
2
4
0
xcos x dx



163/I =
2
0
xcos xsin xdx



164/I =
6
2
0
xcos xsin xdx




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

xe
dx
(x 2)


169/I =
e
1
(1 x)ln xdx


170/I =
e
2
1
xln xdx


171/I =
1
e
2
1
ln xdx


172/I =
e
1
x(2 ln x)dx



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



176/I =
2
5
1
lnx
dx
x


177/I =
e
2
1
e
lnx
dx
(x 1)


178/I =
1
2
0
1x
xln dx
1x




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




.
182/I =
2
4
0
sin2x
dx
1 cos x




183/I =
2
2
1
5
dx
x 6x 9


184/I =
2
1
0
x 3x 2
dx
x3





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

1x




188/I =
1
15 8
0
x 1 x dx


189/I =
x
1
xx
0
e
dx
ee




190/I=
e
1
e
ln x 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





194/I =
2
4
0
1 2sin x
dx
1 sin2x





195/I =
53
3
2
0
x 2x
dx
x1




196/I =
3
2
4
tgx

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 2 x 2)dx

  


200/I =
4
1
2
dx
x 5 4




201/I =
2
1
x
dx
x 2 2 x  



202/I =
2
2
1
ln(1 x)
dx

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





206/I =
2
3
2
1
x1
dx
x



207/I =
3
4
2
0
sin x
dx
cos x



208/I =
2
2
0

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


212/I =
2
1
2
0
x
dx
4x


213/I =
1
2
0
x
dx
4x


214/I =
1
4
2
2
0
x
dx
x1


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






218/I =
3
7
3
2
0
x
dx
1x


219/I =
x
ln2
x
0
1e
dx
1e




220/I =
1

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




224/I =
1
2 2x
0
(1 x) .e dx


225/I =
2
2
0
cosx
dx
cos x 1




226/I =
7
3
3
0
x1
dx
3x 1




.
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

x (1 x) dx


230/I =
3
2
2
0
sin x.cos x
dx
cos x 1




231/I =
1
2
2
0
4x 1
dx
x 3x 2




232*/I =
2
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





236/I =
2
3
0
x1
dx
3x 2




237/I =
4
2
7
1
dx
x x 9


238/I =
34
0
xsin xcos xdx



239/I =

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





242/I =
2
0
sin2x sinx
dx
cos3x 1





243/I =
4
22
0
sin2x
dx
sin x 2cos x




244/I =
2
3
2
2
0

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
2
0
x
dx
4x


248/I =
2
2
2
3
1
dx
x x 1


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
cosx
dx
7 cos2x




252/I =
4
2
1
1
dx
(1 x)x


253/I =
2
3
0
x1
dx

3x 2




254*/I =
3
4
cosx sin x
dx
3 sin2x







.


255/I =
2
3
2
cosx cosx cos xdx







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


259/I =
4
2
0
x.tg xdx



260/I=
2
22
0
1
dx
(4 x )


261/I =
2
1
3
0
3x
dx
x2


262*/I =
5
2

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



265/I =
3
6
0
sin x sin x
dx
cos2x




265/I =
2
3
1
dx
sin x 1 cosx





266/I =
3
62
1
1
dx
x (1 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





270/I =
44
4
0
sin x cos x
dx
sin x cosx 1






271/I =
44
4
0
sin x cos x
dx
sin x cosx 1





272/I =

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
  




275/I =
3
1
23
0
x
dx
(x 1)


276/I =
1
3
0
3
dx
x1


277*/I =
4
1
6
0
x1
dx
x1





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



.

281*/I =
2
1
2
0
xln(x 1 x )
dx
1x




282/I =
4
2
1
(x 1) lnxdx


283/I =
3
2
0
x ln(x 1)dx


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


  


287/I =
1
0
1
dx
x 1 x


288/I =
2
0
cosx
dx
2 cos2x




289/I =
2
4
cosx sin x
dx
3 sin2x







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




293/I =
2
0
1
dx
2 sin x




294/I =
2
0
1
dx
2 cosx





295/I =
2
2
2
3
1
dx
x x 1


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


299/I =
1
2
1
1
dx
1 x 1 x

  




300/I =
3
4
6
1
dx
sin xcosx




301/I =
2
0
cosx
dx

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

dx
cosx 1




305/I =
2
0
1
dx
2cosx sinx 3





306/I =
2
2
3
cosx
dx
(1 cosx)





307/I =

4
3
0
tg x dx





.
308*/I =
1
2x
1
1
dx
3e




309*/I =
2
x
sin x
dx
31






310*/I =
2
0
sin x
dx
cosx sinx




311/I =
4
2
44
0
sin x
dx
cos x sin x




312*/I =
2
2
0
tgx
dx

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

e dx



316*/I =
2
1
2
0
x
dx
x4


317*/I =
3
2
42
0
cos x
dx
cos 3cos x 3




318*/Tìm x> 0 sao cho
2t
x
2

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

5
0
tg x dx



322/I =
4
3
6
cotg x dx




323/I =
3
4
4
tg x dx




324*/I =
4
0
1
dx
2 tgx





325/I =
5
2
0
sin x
dx
cosx 1




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

327*/I =
4
2

0
tgx 1
( ) dx
tgx 1





328*/I =
1
3
1
2
x
dx
x1


329*/I =
3
3
2
4
1
xx
dx
x



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



