[Math] Integral of $\int \sqrt{36t^2 + 144t^4} dt$

Question

$$\int \sqrt{36t^2 + 144t^4} dt$$

I really have no idea how to do this, I tried many types of substitution but it didn't work. I think I can use trig but it won't help much, also my book gives the answer in a form that wouldn't use trig sub. How do I do this?

Answer 1

Hint: Factor out a $t^{2}$ to rewrite the integrand as:

$$\sqrt{t^{2}(36+144t^{2})} = t\sqrt{36+144t^{2}}$$

Then use the appropriate substitution.