integral question substitution

Question

$∫ \dfrac{g(x)g'(x)}{\sqrt{(1+g^2(x))}}$ where $g'(x)$ is continous. I tried use use substitution but I couldn't figure out which one to substitute.

Answer 1

I am attaching the solution of the pic. and go through it. Although you got enough hint.

Answer 2

$g(x)=t$, then you get

$\int \frac{t}{\sqrt{1+t^{2}}}dt=\sqrt{1+t^{2}}+C$,

so

$\int \frac{g(x)g'(x)}{\sqrt{1+g(x)^{2}}}dx=\sqrt{1+g(x)^{2}}+C$