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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

`(2x^(2)-2)/((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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