BA
̀
I TÂ
̣
P TOA
́
N LƠ
́
P 12 Nguyễn Thanh Lam
NGUYÊN HA
̀
M - TI
́
CH PHÂN VA
̀
Ư
́
NG DU
̣
NG
I. NGUYÊN HA
̀
M



( )

 x x dx− +
∫


 
 ÷
 
∫

( ) ( )
 x x x dx+ − +
∫

( )

x x
e e dx
−
−
∫




x
x
e
e dx
x
−
 
+
 ÷
 

 xdx−
∫

( )
  x dx+
∫

( )
  x x dx+
∫

 x xdx
∫

 
  

x
x dx
 
+
 ÷
 
∫

( )
 
 x x dx−
∫


∫

( )

 x dx+
∫

 xdx
∫

 xdx
∫


x x dx+
∫

 
x x dx+
∫



x
e xdx
∫


 xdx
∫

∫

x xdx
∫

x xdx
∫

 xdx
∫

x xdx
∫


x xdx
∫

  x
dx
x
+
∫



 
x
e xdx
∫






xdx
∫


e
dx
x
∫





dx
x
∫


 




x dx
x

π
∫




 xdx
π
∫



 x xdx
π
π
−
∫



   x xdx
π
π
−
∫






−
 ÷
 
∫



 
dx
x x+ + −
∫

( )


 x cos x dx
π
π
−
+
∫

( )


  x cos x dx
π
π
−
∫


 x dx−
∫




 x x dx+ −
∫


 x dx
π
∫


  
o
xdx
π
−
∫




x
xe dx
∫




 xdx
π
∫




 xdx
π
∫



 xdx
π
∫
---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011
BA
̀
I TÂ
̣
P TOA
́
N LƠ
́


x
e xdx
π
∫


 
e
x
dx
x
+
∫





 
x
e xdx
π
∫




 
e


 
x
dx
x
π
+
∫


  

x x dx+
∫


 

a
dx
a x−
∫



x a t
=






x a t
=




 x dx−
∫




 x dx−
∫




 x dx−
∫

 

a
dx
a x+
∫





dx
x x−
∫

  
π π π
 
= −
 ÷
 






x
dx
x
+
−
∫



x t=


∫








x
dx
x
−
−
∫



x
x x
e
dx
e e
−
+
∫








 
xdx
x x+ +
∫




 
dx
x x
π
π
∫

( )

 
e
x
dx
x
π
∫

( )


∫




x
x e dx
−
∫




x xdx
π
∫




x xdx
π
∫




x
e xdx
π



  x x dx−
∫




e
x
dx
x
∫




e
x xdx
∫




x xdx
∫








 

 
x
dx
+
≤ ≤
∫




 
  
dx
x
−
≤ ≤
+
∫





  
x x


 
 
xdx
π
π
π π
≤ + ≤
∫



   
dx
x
π
π π
≤ ≤
+
∫

---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011
BA
̀
I TÂ
̣
P TOA

∫
+
=




π
'(
( )
∫
+=




π
xdxxeI
x
'(
dx
x
x
I
∫
+
+
=




'(
dxxxI
∫
+=




'(
∫
−
+++
−
=




dx
xx
x
I
'(
dxxxI
∫
−=




x
I
'(
∫
−
++
=



xx
dx
I
'(
∫
=
e
dx
x
x
I



'(
dx
x
x
I
∫











π
π
xx
xdxx
J
x
xx
xdx
I
'(
∫
=
e
xdxxI


'(
dxxxI 




'(
∫
−
=
e
xx
dx
I



'(
∫
+
=






π
dx
xx
x
I
'(
∫
+

∫
'(
( )
1
2x
0
I x 2 e dx= −
∫
---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011