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int(dx)/(x^2+2x+2)equals(A) xtan^(-1)(x+...

`int(dx)/(x^2+2x+2)`equals(A) `xtan^(-1)(x+1)+C` (B) `tan^(-1)(x+1)+C`(C) `(x+1)tan^(-1)x+C` (D) `tan^(-1)x+C`

Text Solution

Verified by Experts

The correct Answer is:
b
`int (1)/(x^(2) +2x+2)dx = int (1)/((x^(2)+2x+1)+1)dx`
`= int (1)/((x+1)^(2)+1^(2))dx`
`=tan^(-1) (x+1)+c`
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