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int(x)/((x^2+2x+2)^2)dx=...

`int(x)/((x^2+2x+2)^2)dx=`

A

`(x^2+2)/(x^2+2x+2)-(1)/(2) tan^(-1)(x+1)+c`

B

`(x^2+2)/(2(x^2+2x+2))-(1)/(2)tan^(-1)(x-1)+c`

C

`(x^2-2)/(4(x^2+2x+2))(1)/(2)tan^(-1)(x+1)+c`

D

`(2(x-1))/((x^2+2x+2))+(1)/(2)tan^(-1)(x+1)+c`

Text Solution

Verified by Experts

The correct Answer is:
C
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