I am trying to integrate the following:
$$ \int{\frac{x}{\sqrt{2x^2 + 3}}}dx $$
It seems to me to be a trig substitution; however, I couldn't seem to get it into one of the three forms, i.e., $$\sqrt{a^2 - x^2}$$ $$\sqrt{x^2 - a^2}$$ $$\sqrt{a^2 + x^2}$$
I also tried integration by parts. If I made $u = \frac{1}{\sqrt{2x^2 + 3}}$ and $dv = x$, the next integral was more complicated, and if I made $u = x$ and $dv = \frac{1}{\sqrt{2x^2 + 3}}$, I was again unsure how to integrate the 1/sqrt term.
How do I solve this?