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. Putting x = t 3 and dx = 3t 2 dt, we get
I = 
.3t 2 dt
= 3 
dt
= 3 
dt
= 3 
dt
= 
+ 3 
dt
Let 
= 
+ 
⇒ A(t 2 – t + 1) + (Bt + C) (t + 1) = t 2 – t
On equating the coefficient of like powers of t, we get
A + B = 1, –A + C + B = –1, A + C = 0
⇒ A = 
, B = 
, C = – 
= 
+ 
Hence,
I = 
t 2 + 2 
dt + 
dt
= 
t 2 + 2 log (t + 1) + 
dt
= 
t 2 + 2 log (t + 1) + 
dt
– 
dt
= 
t 2 + 2 log (t + 1) + 
log (t 2 – t + 1)
– 
tan –1 
+ C
= 
x 2/3 + 2 log (x 1/3 + 1) + 
log (x 2/3 – x 1/3 + 1)
– 
tan –1 
+ C
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