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int (x^3-1)/((x^4+1)(x+1)) dx is...

`int (x^3-1)/((x^4+1)(x+1)) dx` is

A

`(1)/(4)ln(1+x^(4))+(1)/(3)ln(1+x^(3))+c`

B

`sinx|-sinx+C`

C

`(1)/(4)ln(1+x^(4))-ln(1+x)+c`

D

`(1)/(4)ln(1+x^(4))+ln(1+x)+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`int(x^(3)-1)/((x^(4)+1)(x+1))dx=int((x^(4)+x^(3))-(x^(4)+1))/((x^(4)+1)(x+1))dx`
`=int(x^(3))/(x^(4)+1)dx-int(1)/(x+1)dx`
`=(1)/(4)ln(x^(4)+1)-ln(x+1)+c`
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