Integral of $\frac{x^2}{\sqrt{x^2+5}}$

Question

I need help with this integral:

$$I = \int \frac{x^2}{\sqrt{x^2+5}}\, dx$$

I substituted $x = \sqrt{5}\tan{\theta}$, and reached $$I = 5\int \frac{\sin{(\theta)}^2}{\cos{(\theta)}^3}\,d\theta$$ which I'm unable to solve.
For context this is in an exercise of trig substitution, and I'm not allowed to use the secant reduction formula which WolframAlpha suggests I use.

Answer 1

Hint: (Use hyperbolic trigonometric substitution to) $$ \frac{x^2}{\sqrt{x^2+5}}=\sqrt{x^2+5}-\frac{5}{\sqrt{x^2+5}}. $$