치환적분

$\displaystyle \sin \left( x - \frac{\pi}{4} \right) = t$로 놓으면 $\displaystyle \frac{dt}{dx} = \cos \left( x - \frac{\pi}{4} \right)$ $\displaystyle x = \frac{\pi}{4}$일 때 $t = 0$, $\displaystyle x = \frac{3 \pi}{4}$일 때 $t = 1$이므로 $\displaystyle \int _{\frac{\pi}{4}} ^{\frac{3 \pi}{4}} {} \cos \left( x - \frac{\pi}{4} \right) e ^{\sin \left( x - \frac{\pi}{4} \right)} dx$$\displaystyle = \int _{0} ^{1} {} e ^{t} dt$$\displaystyle = \left[ \begin{array}{l} \begin{matrix} \\ \end{matrix} e ^{t} \end{array} \right] _{0} ^{1}$$= e - 1$