Question

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

Answer 1

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