Algebraic Substitution Of Fractions I already tried to putting the square root like this: $\sqrt{\frac{x}{5 + x}}$ but I dont know what to do next.
$$\int \frac{\sqrt{x}}{\sqrt{5+x}}dx$$

$$\frac x{5+x}=u^2\implies x=\frac{5u^2}{1-u^2}\implies dx=\frac{10u\,du}{(1-u^2)^2}\implies$$
$$\int\sqrt\frac x{5+x}\,dx=\int\frac{10u^2}{(1-u^2)^2}du$$
and now you have the integral of a rational function. Do, for example, partial fractions, or whatever.
