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

MCQ

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

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

Correct option: B.

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

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

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