Q.Evaluate: $\int \csc(\log x)\left[1-\cot(\log x)\right]dx$

Because $\frac{d}{dx}[e^xf(x)]=e^xf(x)+e^xf'(x)=e^x[f(x)+f'(x)]$, any integrand that can be written as $e^x$ multiplied by "some function $f(x)$ plus its own derivative $f'(x)$" integrates immediately to $e^xf(x)+c$, without any e …