Hints to find a certain integral How can I find $\int\sqrt{x}/(x^2+1)\,dx$?
I tried by substitution and by integration by parts but it doesn't seem to work. I only need hints, not answers.

Try taking
$$u=\sqrt{x}\text{ and }du=\dfrac{1}{2\sqrt{x}}\,dx$$
Then you get
$$2\int\frac{u^2}{u^4+1} \, du$$
Can you take it from here?
