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int(x^(4)+1)/(x^(6)+1)dx is equal to...

`int(x^(4)+1)/(x^(6)+1)dx` is equal to

A

`tan^(-1)x+(1)/(3)tan^(-1)x^(3)+C`

B

`tan^(-1)x-(1)/(3)tan^(-1)x^(3)+C`

C

`-tan^(-1)x-(1)/(3)tan^(-1)x^(3)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
`I=int(x^(4)+1)/(x^(6)+1)dx=int((x^(4)-x^(2)+1)+x^(2))/(x^(6)+1)dx`
`rArr I=int(x^(4)-x^(2)+1)/((x^(2))+1)dx+int(x^(2))/(x^(6)+1)dx`
`rArr I= int(1)/(x^(2)+1)dx+(1)/(3)int(1)/((x^(3))^(2)+1)d(x^(3))`
`rArr I=tan^(-1)x+(1)/(3)tan^(-1)(x^(3))+C`
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