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int e^x((x^2+1))/((x+1)^2)dx is equal to...

`int e^x((x^2+1))/((x+1)^2)dx` is equal to
(a) `((x-1)/(x+1))e^x+c`
(b) `e^x((x+1)/(x-1))+c`
`e^x(x+1)(x-1)+c`
(d) none of these

A

`((x-1)/(x+1))e^(x)+c`

B

`e^(x)((x+1)/(x-1))+c`

C

`e^(x)(x+1)(x-1)+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`int (e^(x)(x^(2)+1))/((x+1)^(2))dx=int (e^(x)(x^(2)-1+2))/((x+1)^(2))dx`
`=int e^(x)[(x-1)/(x+1)+(2)/((x+1)^(2))]dx`
`=int e^(x)[f(x)+f'(x)]dx,`
`=e^(x)((x-1)/(x+1))+C`
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