Evalute : 1 7+6 x-x^2 d x - Vidyadip

Question

Evalute : $\int \frac{1}{7+6 x-x^2} d x$

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Answer

$
\begin{aligned}
& \int \frac{1}{7+6 x-x^2} d x \\
= & \int \frac{1}{7-\left(x^2-6 x+9\right)+9} d x \\
= & \int \frac{1}{(4)^2-(x-3)^2} d x \\
= & \frac{1}{2 \times 4} \log \left|\frac{4+x-3}{4-x+3}\right|+c \\
= & \frac{1}{8} \log \left|\frac{1+x}{7-x}\right|+c .
\end{aligned}
$

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