Evaluate : d x x^2-3 x+2 - Vidyadip

MCQ

Evaluate : $\int \frac{d x}{\sqrt{x^2-3 x+2}}$

A
$\log \left|\left(x+\frac{3}{2}\right)+\sqrt{x^2-3 x+2}\right|+C$
B
$\log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^2-3 x+2}\right|+C$
C
$\log \left|\left(x-\frac{3}{2}\right)-\sqrt{x^2-3 x+2}\right|+C$
D
$\log \left|\left(x+\frac{3}{2}\right)-\sqrt{x^2-3 x+2}\right|+C$

✓

Answer

$\begin{array}{l}\text { (b) : We have, } \int \frac{d x}{\sqrt{x^2-3 x+2}}=\int \frac{d x}{\sqrt{\left(x^2-3 x+\frac{9}{4}\right)-\frac{1}{4}}} \\ =\int \frac{d x}{\sqrt{\left(x-\frac{3}{2}\right)^2-\left(\frac{1}{2}\right)^2}}=\log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^2-3 x+2}\right|+C\end{array}$

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