Помогите , срочно ! π/6 ∫ ^ecosx·sinx dx = 0

Решите задачу:

$\int\limits_0^\frac{\pi}{6}e^{cosx}sinxdx\\\\\int e^{cosx}sinxdx\Rightarrow \left|\begin{array}{ccc}cosx=t\\-sinxdx=dt\\sinxdx=-dt\end{array}\right|\Rightarrow-\int e^tdt=-e^t=-e^{cosx}\\-----------------------------\\\\\int\limits_0^\frac{\pi}{6}e^{cosx}sinxdx=\left-e^{cosx}\right]^\frac{\pi}{6}_0=-e^{cos\frac{\pi}{6}}-\left(-e^{cos0}\right)=-e^\frac{\sqrt3}{2}+e^1\\=e-e^\frac{\sqrt3}{2}$