Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Integrate, 
dx
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
tan -1 x – 
n (1 + x) + 
n (1 + x 2 ) + 
+ C
Sol. Ι = 
= 
= 
+ 
......(i)
Again 
= 
+ 
⇒ x = (Ax + B)(x + 1) + C(x 2 + 1)
Putting x = – 1 ⇒ C = – 1/2
Equating coefficient of x 2 , we get
0 = A + C ⇒ A = – C = 1/2
Putting x = 0, we obtain
0 = B + C ⇒ B = – C = 1/2
Therefore,
= 
– 
+ 
Ι = – 
= – 
where 
Let x = tan θ , so that dx = sec 2 θ d θ
Ι 1 = 
= 
= 
= 
= 
Hence Ι = 
tan -1 x – 
n (1 + x) + 
n (1 + x 2 ) + 
+ C
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