Question

$\int \frac{dx}{x^2+4x+13}$ is equal to

• A. $\log (x^2+4x+13)+c$
• B. $\frac{1}{3}{\tan }^{-1}\left(\frac{x+2}{3}\right)+c$
• C. $\log (2x+4)+c$
• D. $\frac{2x+4}{(x^2+4x+13)}+c$

Answer 1

Answer: (B)

Let $I=\int \frac{dx}{4x^2+4x+13}$
$=\int \frac{dx}{x^2+4x+4+9}$
$=\int \frac{dx}{{(x+2)}^2+3^2}$
$=\frac{1}{3}{\tan }^{-1}\left(\frac{x+2}{3}\right)+c$