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

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

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

Text Solution

Verified by Experts

The correct Answer is:
B
`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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