Question

integration of
$xdx \div \sqrt {x }^{2} - 2$
​

Answer 1

Answer:

$\sqrt{x^2-2}$

Explanation:

The question is

$I=\int \frac{xdx}{\sqrt{x^2-2}}$

Let $x^2-2=t$

Then, $2xdx=dt$

Therefore,

$I=\int \frac{dt}{2\sqrt{t}}$

$\implies I=\frac{1}{2}\int t^{-1/2}dt$

$\implies I=\frac{1}{2}\times\frac{t^{1/2}}{1/2}$

$\implies I=\frac{1}{2}\times 2\times \sqrt{x^2-2}$

$\implies I=\sqrt{x^2-2}$

Hope this answer is helpful.