JEE Mathematics/ Lakshmikanta Satapathy/ Questions on Indefinite Integration part 12 taken from previous Board papers solve by the method of substitution using standard Integrals

1. Physics Helpline
L K Satapathy
Indefinite Integrals 12

2. Physics Helpline
L K Satapathy
Indefinite Integrals - 12
Answer-1 ( )( )
. .
( )( )
a x a x a x
I dx dx
a x a x a x
  
 
   
2 2
2 , 2 . .
2
dt
For I Put a x t x dx dt x dx      Substitution :
1 22 2 2 2 2 2
.
. .
a x a x dx
dx dx I I
a x a x a x
 
    
  
  
1
1 2 2
sin
dx x
I a a
aa x

  

 2 2 2
.x dx
and I
a x




2 2
2
2
dt
I t C a x C
t
      
1 2 2
1 2 [s ]in
x
I I I a a AnC sx
a

      

3. Physics Helpline
L K Satapathy
Indefinite Integrals - 12
Answer-2
Substitution : 2 2
tan sec . sec .
dt
Put a x t a x dx dt x dx
a
    
2
2 2 2 2 2 2 2
sec .
sin cos tan
dx x dx
I
a x b x a x b
 
  
2 2
1 dt
I
a t b


11 1
tan
t
C
a b b
 
  
 
1
[ ]
1 tan
tan
a x
C
ab b
Ans  
  
 
11
tan
t
C
ab b

 
1
2 2
1
tan
dx x
using C
x a a a
  
    


4. Physics Helpline
L K Satapathy
Indefinite Integrals - 12
Answer-3
2
16 6
dx
I
x x

 

2
25 ( 6 9)
dx
x x

  

2
25 9 6
dx
x x

  

2 2
5 ( 3)
dx
x

 

1
[
3
sin
5
]
x
C Ans  
  
 
1
2 2
sin
dx x
using C
aa x
  
  
 


5. Physics Helpline
L K Satapathy
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