int frac{d x}{x^{2}+2 x+2} equals | vedclass

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Question

(C) To evaluate the integral $\int \frac{d x}{x^{2}+2 x+2}$,we first complete the square in the denominator.$x^{2}+2 x+2 = (x^{2}+2 x+1) + 1 = (x+1)^{

Vedclass · Accepted Answer

$	an ^{-1}(x+1)+C$

Vedclass · Answer

(C) To evaluate the integral $\int \frac{d x}{x^{2}+2 x+2}$,we first complete the square in the denominator.$x^{2}+2 x+2 = (x^{2}+2 x+1) + 1 = (x+1)^{2} + 1^{2}$.Now,the integral becomes $\int \frac{d x}{(x+1)^{2} + 1^{2}}$.Using the standard integration formula $\int \frac{d u}{u^{2} + a^{2}} = \frac{1}{a} 	an^{-1}(\frac{u}{a}) + C$,where $u = x+1$ and $a = 1$,we get:$\int \frac{d x}{(x+1)^{2} + 1^{2}} = 	an^{-1}(x+1) + C$.Thus,the correct option is $C$.

$\int \frac{d x}{x^{2}+2 x+2}$ equals

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