How to integrate a product of three terms? (includes an exponential and trig. function) Given a periodic signal with $T=2$, I need to find the complex Fourier coefficient $C_n$, using the following formula:
$$C_n = \frac 1 T \int_\frac {-T} 2^\frac T 2 f(t) \, e^{-jnwt} dt$$
where
$$f(t)=t^2 \cos(3 \pi t)$$
My integral becomes a product of three terms. I tried to look this integral up in integral tables online but could not find anything. Closest I could find is #107 from http://integral-table.com/downloads/single-page-integral-table.pdf Does a formula exist for this particular integral?

In my humble opinion, I think that the easiest is to consider two integrals
$$A=\int t^2 \cos(3 \pi t) \, e^{-inwt}\, dt\qquad \text{and}\qquad B=\int t^2 \sin(3 \pi t) \, e^{-inwt} \,dt$$ and use
$$C=A+iB=\int t^2 e^{i 3 \pi t} \, e^{-inwt}\, dt=\int t^2 e^{i  (3 \pi -n \omega )t}\,dt$$ 
To make life easier, let $$x=i  (3 \pi -n \omega )t\implies C=\frac{i }{(3 \pi -n \omega )^3}\int{  x^2 e^x}\,dt$$
Now, two integrations by parts  to get the integral; when done, replace $x$, redecompose $A$  and finally use the given integration bounds.
