Question

Solve :
$\int \frac{dx}{x^2+8x+20}$

Answer 1

Consider the given integral.

$I=\int \frac{dx}{x^2+8x+20}$

$I=\int \frac{dx}{x^2+8x+16+4}$

$I=\int \frac{dx}{(x+4{)}^2+2^2}$

We know that

$\int \frac{dx}{x^2+a^2}=\frac{1}{a}{\tan }^{-1}\frac{x}{a}+C$

Therefore,

$I=\frac{1}{2}{\tan }^{-1}\frac{x+4}{2}+C$

Hence, this is the answer.