Question

$\int \frac{1}{x^2+6x+13}dx$

Answer 1

$$\begin{gathered} \int \frac{dx}{x^2+6x+13} \\ =\int \frac{dx}{x^2+2\times x\times 3+9-9+13} \\ =\int \frac{dx}{{\left(x+3\right)}^2+2^2} \\ =\frac{1}{2}{\tan }^{-1}\left(\frac{x+3}{2}\right)+C \end{gathered}$$