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int(x^3-x)/(1+x^6)dx is equal to...

`int(x^3-x)/(1+x^6)dx` is equal to

A

`(1)/(6)log.(x^(4)-x^(2)+1)/(x(x^(2)+1))+C`

B

`(1)/(6)tan^(-1).((x^(2)+1)^(2))/(2)+C`

C

`log.(x^(4)-x^(2)+1)/((1+x^(2))^(2))+C`

D

`tan^(-1).((x^(2)+1)^(2))/(2)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=(1)/(2)int(t-1)/(1+t^(3))dt (" where "t=x^(2))`
`=(1)/(2)int((-2)/(3(1+t))+(1)/(3)((2t-1))/(t^(2)-t+1))dt " (After partial fractions)"`
`=(1)/(6).ln(x^(4)-x^(2)+1)/((x^(2)+1)^(2))+C`
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