Question

$\int \frac{dx}{\sqrt{9x^2-6x+2}}$

Answer 1

$\int \frac{dx}{\sqrt{9x^2-6x+2}}$

$\int \frac{dx}{\sqrt{(3x-1{)}^2+1}}$

Let $3x-1=u$

$⟹3dx=du$

$\int \frac{1}{3}\frac{dx}{\sqrt{u^2+1}}$

This is a standard integral

$⟹\frac{1}{3}ln|(\sqrt{u^2+1}+u)|+c$

$⟹\frac{1}{3}ln|(\sqrt{(3x-1{)}^2+1}+3x-1)|+c$