Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Evaluate 
dx
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. We have, I = 
dx
Putting tan x = t and sec 2 x dx = dt, we get
I = 
× 
= 
dt
Let 
= 
+ 
⇒ t = (At + B) (t 2 + 4t + 1) + (Ct + D) (t 2 + 1)
On equating coefficients of like powers of t on both sides, we get
0 = B + D
1 = 4B + A + C
0 = B + 4A + D
and, 0 = A + C
Solving these equations, we get
A = 0, B = 
, C = 0 and D = – 
∴ 
= 
– 
⇒ I = 
dt – 
dt
= 
dt – 
dt
= 
tan –1 (t) – 
log 
+ C
= 
x – 
log 
+ C
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