Evaluate the integral .

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Evaluate the integral

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

. (i) Express the denominator

x^{2}+6x+13

in completed–square form. (ii) Hence, find the indefinite integral

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

, simplifying your final answer as far as possible.