JEE Mathematics / Lakshmikanta Satapathy / Anti-derivative formulae for Polynomial, trigonometric , inverse trigonometric, logarithmic and exponential functions

1. Physics Helpline
L K Satapathy
Integration Formulae 1

2. Physics Helpline
L K Satapathy
1
(1) ( ) ( 1).n nd
x n x
dx

 
Anti-derivatives :
Integration Formulae -1
  1
(2)
2
d
x
dx x

1
(3) (log )
d
x
dx x

(4) ( )x xd
e e
dx

(5) ( ) .logx xd
a a a
dx

1
. , 1
1
n
n x
x dx C n
n

    

1
. 2dx x C
x
  
1
. logdx x C
x
  
.x x
e dx e C  
.
log
x
x a
a dx C
a
  

3. Physics Helpline
L K Satapathy
Anti-derivatives :
Integration Formulae -1
(6) (sin ) cos
d
x x
dx

(7) (cos ) sin
d
x x
dx
 
(8) (sec ) sec .tan
d
x x x
dx

(9) (cosec ) cosec .cot
d
x x x
dx
 
2
(10) (tan ) sec
d
x x
dx

2
(11) (cot ) cosec
d
x x
dx
 
cos . sinx dx x C  
sin . cosx dx x C   
sec .tan . secx x dx x C  
cosec .cot . cosecx x dx x C   
2
sec . tanx dx x C  
2
cosec . cotx dx x C   

4. Physics Helpline
L K Satapathy
Integration Formulae -1
Anti-derivatives :
1
2
1
(12) (sin )
1
d
x
dx x



1
2
1
(13) (cos )
1
d
x
dx x
 


1
2
1
(14) (tan )
1
d
x
dx x



1
2
1
(15) (cot )
1
d
x
dx x
 


1
2
1
(16) (sec )
1
d
x
dx x x



1
2
1
(17) (cosec )
1
d
x
dx x x
 


1
2
1
. sin
1
dx x C
x

  


1
2
1
. cos
1
dx x C
x

  


1
2
1
. tan
1
dx x C
x

  

1
2
1
. cot
1
dx x C
x

  

1
2
1
. sec
1
dx x C
x x

  


1
2
1
. cosec
1
dx x C
x x

  



5. Physics Helpline
L K Satapathy
Integration Formulae -1
Anti-derivatives :
1
(18) (logsin ) .cos cot
sin
d
x x x
dx x
 
2
sec tan sec
(20) log(sec tan ) sec
sec tan
d x x x
x x x
dx x x

  

sec . log sec tanx dx x x C   
2
cosec cot cosec
(21) log(cosec cot ) cosec
cosec cot
d x x x
x x x
dx x x
 
  

cosec . log cosec cotx dx x x C   
cot . log sinx dx x C  
1
(19) (logcos ) .( sin ) tan
cos
d
x x x
dx x
   
tan . log cos log secx dx x C x C     

6. Physics Helpline
L K Satapathy
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