Bang cong thưc nguyen ham

CÔNG THỨC NGUYÊN HÀM

0dx C



dx x C 



 

1

x

x dx C 1

1





   

 



 

 

 

1 1 1

(x a) (x a) dx C 1

1

1 (ax b) (ax b) dx C 1

a 1 u

u du C 1

1















    

 



    

 

   

 







1

dx ln x C

x  



1

dx ln x a C

x a

1 1

dx ln ax+b C ax+b a

1

du ln u C u

  



 







e dx e C



e dx e C

1

e dx e C

a

e du e C

 

 

 







x

a dx C

ln a

 



x n

x n

mx+n mx+n

u u

a

a dx C

ln a

1 a

a dx C

m ln a a

a du C

ln a



 







cos xdx sin x C 



cos(x+a)dx sin(x+a) C

1 cos ax.dx sin ax C

a 1 cos(ax+b)dx sin(ax+b) C

a cosu du sinu C

 









sin xdx cos x C



sin(x a)dx cos(x a) C

1 sin axdx cos ax C

a 1 sin(ax b)dx cos(ax b) C

a sinu du cosu C

   

 

    

 









1

dx tan x C

cos x  



2 2 2 2

1

dx tan(x a) C cos (x a)

dx tan ax C cos ax a

dx tan(ax+b) C cos (ax+b) a

1

du tanu C cos u

  



 









2

1

dx cot x C

sin x  



2 2 2 2

1

dx cot(x a) C sin (x a)

dx cot ax C sin ax a

dx cot(ax+b) C sin (ax+b) a

1

du cotu C sin u

  



 

  

 









t anxdx ln cosx C



t an(x+a)dx ln cos(x+a) C

1

t an(ax)dx ln cosax C

a 1

t an(ax+b)dx ln cos(ax+b) C

a tan udu ln cosu C

 









cotxdx ln sinx C 



cot(x+a)dx ln sin(x+a) C

1 cot(ax)dx ln sinax C

a 1 cot(ax+b)dx ln sin(ax+b) C

a cot udu ln sinu C

 









dx ln C (a b) (x a)(x b) b a x b





dx ln C (a b) (x a)(b x) b a b x





dx ( )dx (ax b)(cx d)   ax b cx d  

dx ( )dx (ax b)(cx d)   ax b cx d  

sau đó tìm A, B bằng cách đồng nhất 2 tử số