Question

Integration by parts problem

Answer 1

\[\int\limits_{?}^{?} x^2\cos(mx)dx\]

Answer 2

I put the following
u= x^2
du=2xdx
v=sin(mx)/m
dv=cos(mx)

Answer 3

\[ \int f (x) g(x) dx = f \int gdx - \int \frac{df}{dx}\left( \int g dx \right)dx \]
put f=x^2 ... use by parts two times.

Answer 4

In case it helps you, I can also recommend you to use the tabular method for such a problem.