∫_0^ π / 4 x e^ x d x is equal to

Suppose, $I=\int_0^{\pi / 2} \cos x e^{\sin x} d x<br />Let$\sin x=t \Rightarrow \cos x d x=d t$<br />$x \rightarrow 0 \Rightarrow t \rightarrow 0$<br />and$x \rightarrow \frac{\pi}{2} \Rightarrow t \rightarrow 1$<br />So$I=\int_0^1 e^t d t=\left[e^t\right]_0^1=e-1