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int(x^3)/((1+x^8)) dx...

`int(x^3)/((1+x^8)) dx`

A

`tan^(-1)x^(4)+C`

B

`4tan^(-1)x^(4)+C`

C

`(1)/(4)tan^(-1)x^(4)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Put `x^(4)=t and4x^(3)dx=dt`.
`:." "I=(1)/(4)int(dt)/((1+t^(2)))=(1)/(4)tan^(-1)t+C=(1)/(4)tan^(-1)x^(4)+C`.
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