[Math] How to evaluate the integral $\int_0^1 t\sqrt{4+9t^2} \,dt$

Question

Can somebody please show me how to evaluate the following integral:
$$\int_0^1 t\sqrt{4+9t^2} \,dt?$$

I know how to integrate a square root function, but the $t$ in front throws me off, and if there are associated properties with this sort of integral.

Could you also, knowing that $t=\sqrt{t^2}$, multiply it into the other square root and integrate that way?

Answer 1

Hint: Substitute $u = 4 + 9t^2$, $du = 18 t dt$.