int frac{dx}{x^2 + 2x + 2} = | vedclass

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Question

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

Vedclass · Accepted Answer

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

Vedclass · Answer

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

$\int \frac{dx}{x^2 + 2x + 2} = $

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