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

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

CBSE Class 12 · 2006 · Indefinite IntegralsVery Short Answer

Evaluate :

\int \frac{d x}{x ^{2} - 3 x + 2}

Answer: $lo g x - \frac{3}{2} + x^{2} - 3 x + 2 + C$

Complete the square in the radicand:

x^{2} - 3 x + 2 = (x - \frac{3}{2})^{2} - \frac{1}{4} .

This is the standard form

\frac{d x}{u ^{2} - a ^{2}}

with

u = x - \frac{3}{2}

a = \frac{1}{2}

\int \frac{d x}{( x - \frac{3}{2} ) ^{2} - ( \frac{1}{2} ) ^{2}} = lo g (x - \frac{3}{2}) + x^{2} - 3 x + 2 + C .

lo g x - \frac{3}{2} + x^{2} - 3 x + 2 + C

CBSE Class 12 Board · 2006 · Subjective