Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Integrate with respect to x :
(i) 
(ii) 
(iii) 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(i) 
tan –1 
– 
n 
+ C
(ii) 
tan –1 
+ C
(iii) – 
n 
+ C
Sol. (i) Ι = 
dx = 
= 
– 
= 
where u = x – 1/x ⇒ 
= du
and v = x + ⇒ 
dx = dv
Ι = 
tan –1 
– 
n 
+ C
= 
tan –1 
– 
n 
+ C
(ii) Ι = 
= 
= 
Put x – 
= t ⇒ 
dx = dt
⇒ Ι = 
= 
tan –1 
+ C = 
tan -1 
+ C
(iii) Ι = 
= 
= – 
Put x + 
= t ⇒ 1 – 
= dt
⇒ Ι = – 
= – 
log 
+ C
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