Let $$A_n(x)=\int x^n\sin(4x)$$ and $$v'=\sin(4x)$$
Using Integration by Parts, we get $$A_n(x)=-\frac{x^n\cos(4x)}{4}+\int\frac{nx^{n-1}\cos(4x)}{4}$$
Using Integration by Parts on this new integral, and letting$$v'=\frac{\cos(4x)}{4}$$we get $$A_n(x)=-\frac{x^n\cos(4x)}{4}+\frac{nx^{n-1}\sin(4x)}{16}+!!!\int\frac{\sin(4x)(n-1)nx^{n-2}}{16}!!!$$
I'm fairly sure that this is alright so far (the first two fractions are being shown as correct), but the problem is that the submission system requires the last integral (between the !!!'s) to be calculated and in the form of $$(integral solution)A_{n-2}(x)$$ I'm pretty much stuck at this point, calculating the integral with two variables isn't something I've done before, and so far none of my attempts have worked.
Please note that the $A_{n-2}(x)$ at the very end is hardcoded into the submission, so the answer needs to be in that format.