int (x^3-1)/(x^3+x) dx=...

`int (x^3-1)/(x^3+x) dx=`

A

`x-log_(e)|x|+log_(e)(x^(2)+1)-tan^(-1)x+C`

B

`x-log_(e)|x|+(1)/(2)log_(e)(x^(2)+1)-tan^(-1)x+C`

C

`x+log_(e)|x|+(1)/(2)log_(e)(x^(2)+1)+tan^(-1)x+C`

D

none of these

Verified by Experts

`int(x^(3)-1)/(x^(3)+x)dx=int(1+(1)/(1+x^(2))-(1)/(x)+(x)/(x^(2)+1))dx`
`=x-tan^(-1)x-log_(e)|x|+(1)/(2)log_(e)(x^(2)+1)+C`

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