Integration of fraction with square root I have a problem with integrating of fraction
$$
\int \frac{x}{x^2 + 7 + \sqrt{x^2 + 7}}
$$
I have tried to rewrite it as $\int \frac{x^3 + 7x - x \sqrt{x^2 + 7}}{x^4 + 13x^2 + 42} = \int \frac{x^3 + 7x - x \sqrt{x^2 + 7}}{(x^2 + 6)(x^2 + 7)}$ and then find some partial fractions, but it wasn't succesful.

Since $x^2 + 7$ shows up twice it would make a good first substitution. If $u = x^2 + 7$ then 
$$\int \frac{x}{x^2 + 7 + \sqrt{x^2 + 7}} \, dx = \frac 12 \int \frac{1}{u + \sqrt{u}} \, du.$$
Can you take it from there?
