Integral I think

Calculus Level 5

$\large \int_{0}^{\infty } \frac{\log ^3(t) \sin ^3(t)}{t^{3/2}} \ dt$

Compute the closed form of the integral above to four decimal places.

1 solution

Christopher Criscitiello
Nov 24, 2017

Here are some hints for one way to do this:

(1) Reduce the integral to $\displaystyle\int_0^{\infty } \sin ^3(t) t^{a x} \, dt$ using differentiation under the integral.

(2) You can use contour integration to handle $\displaystyle\int_0^{\infty } t^x \sin (t) \, dt$ .