This discussion is now closed.
\displaystyle uv - \int v \hspace{5} du
[br]\displaystyle \int_{-\pi}^{\pi}e^{x}\cos(nx)dx\\[br]=\ [e^{x}\cos(nx)]_{-\pi}^{\pi} + n\int_{-\pi}^{\pi}e^{x} \sin(nx)dx \\[br]=\ (-1)^n(e^{\pi}-e^{-\pi}) + n \left( [e^{x}\sin(nx)]_{-\pi}^{\pi} - n\int_{-\pi}^{\pi}e^{x} \cos(nx)dx \right)\\[br]=\ (-1)^n(e^{\pi}-e^{-\pi}) - n^2 \int_{-\pi}^{\pi}e^{x} \cos(nx)dx \right)[br]
\displaystyle[br]\int_{-\pi}^{\pi} \sinh(x)\sin(nx) dx\\[br]=\ [\cosh(x)\sin(nx)]_{-\pi}^{\pi} - n\int_{-\pi}^{\pi} \cosh(x)\cos(nx) dx\\[br]=\ -n \left( [\sinh(x)\cos(nx)]_{-\pi}^{\pi} + n\int_{-\pi}^{\pi} \sinh(x)\sin(nx) dx \right) \\[br]=\ -n(-1)^{n}(\sinh(\pi) - \sinh(-\pi)) - n^2 \int_{-\pi}^{\pi} \sinh(x)\sin(nx) dx[br]