intx^3/(x+1)dxis equal to:...

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

A

`x+(x^(2))/(2)+(x^(3))/(3)-log|1-x|+C`

B

`x+(x^(2))/(2)-(x^(3))/(3)-log|1-x|+C`

C

`x-(x^(2))/(2)-(x^(3))/(3)-log|1+x|+C`

D

`x-(x^(2))/(2) + (x^(3))/(3) - log|1+x|+C`

Text Solution

Verified by Experts

The correct Answer is:

A

Let ` I = int(x^(3))/(x+1)dx`
`= int (x^(2) - x + 1) - (1)/((x+1))dx`
` = (x^(3))/(3) - (x^(2))/(2) + x - log |x+1|+C`

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