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

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)2 Marks
Question
Evalute : $\int \sqrt{x^2-8 x+7} d x$
✓

Answer

$
\begin{aligned}
& \int \sqrt{x^2-8 x+7} d x \\
= & \int \sqrt{\left(x^2-8 x+16\right)-9} d x \\
= & \int \sqrt{(x-4)^2-(3)^2} d x \\
= & \frac{(x-4)}{2} \sqrt{(x-4)^2-(3)^2}- \\
& \frac{(3)^2}{2} \log \left|(x-4)+\sqrt{(x-4)^2-(3)^2}\right|+c \\
= & \frac{(x-4)}{2} \sqrt{x^2-8 x+7}- \\
& \frac{9}{2} \log \left|(x-4)+\sqrt{x^2-8 x+7}\right|+c .
\end{aligned}
$

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