Evalute : 1 x^2+4 x-5 d x - Vidyadip

Question

Evalute : $\int \frac{1}{x^2+4 x-5} d x$

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Answer

$
\begin{aligned}
& \int \frac{1}{x^2+4 x-5} d x \\
= & \int \frac{1}{\left(x^2+4 x+4\right)-4-5} d x \\
= & \int \frac{1}{(x+2)^2-(3)^2} d x \\
= & \frac{1}{2 \times 3} \log \left|\frac{x+2-3}{x+2+3}\right|+c \\
= & \frac{1}{6} \log \left|\frac{x-1}{x+5}\right|+c .
\end{aligned}
$

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