Correct Answer - `e^xcotx`
`inte^x(cotx-cosec^2x)dx =inte^xcotxdx-inte^xcosec^2x dx`
`=int[e^xcotx dx-[e^x int cosec^2x dx -int{d/(dx)e^x int cosec^2xdx}]dx`
`int e^xcot x dt -{e^x(-cotx)+inte^xcotx dx}`
`=int e^xcot x dx +e^x cot x-int e^(x)cotx dx =e^x cotx`
