Evaluate: ∫ eˣ csc x (1 - cot x) dx

$\int e^x \csc x (1 - \cot x)\,dx$ $= \int e^x(\csc x - \csc x \cot x)\,dx$ $= \int e^x(\csc x + (-\csc x \cot x))\,dx$ $[\because \int e^x(f(x) + f'(x))\,dx = e^x f(x) + c]$ $= e^x \csc x + c$