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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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