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Integration (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)1 Mark
Question
Evalute : $\int \frac{d x}{9 x^2-25}$
✓

Answer

$
\begin{aligned}
& \int \frac{d x}{9 x^2-25}=\frac{1}{9} \int \frac{1}{x^2-\frac{25}{9}} d x \\
= & \frac{1}{9} \int \frac{1}{x^2-\left(\frac{5}{3}\right)^2} d x \\
= & \frac{1}{9} \times \frac{1}{2 \times \frac{5}{3}} \log \left|\frac{x-\frac{5}{3}}{x+\frac{5}{3}}\right|+c \\
= & \frac{1}{30} \log \left|\frac{3 x-5}{3 x+5}\right|+c .
\end{aligned}
$

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