Find the value of the integral .

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Find the value of the integral

\displaystyle\int \frac{dx}{\sqrt{9-6x-x^{2}}}

. (i) Rewrite the quadratic expression

9-6x-x^{2}

so that the radicand is expressed in the form

a^{2}-(x-h)^{2}

, where

a

and

h

are constants. (ii) Hence, evaluate

\displaystyle\int \frac{dx}{\sqrt{9-6x-x^{2}}}