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

Question

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

✓

Answer

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

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