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int1/(x^(2)+2x+2)^(2)dx=...

`int1/(x^(2)+2x+2)^(2)dx=`

A

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

B

`1/2[sec^(-1)(sqrt(x+1))+(x+1)/(x^(2)+2x+2)]+c`

C

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

D

`(sec^(-1)(sqrt(x+1)))/2+(x+1)/(x^(2)+2x+2)+c`

Text Solution

Verified by Experts

The correct Answer is:
C
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