第4.5問

以下の式を求めてください．
${\displaystyle {\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{e}^{\pi t-\frac{e^{\pi t}}{\sqrt{2}}}\frac{({\left(4t\right)}^2+15)\cos \frac{e^{\pi t}}{\sqrt{2}}-8t\sin \frac{e^{\pi t}}{\sqrt{2}}}{{({\left(4t\right)}^2+15)}^2+{\left(8t\right)}^2}\mathrm{d}t}$