Question

Evaluate the integral: dx / e^(pie*x) from 2 (upper bound) to 0.

Answer 1

Substitution:
u = - π x
d u = - π d x
d x = - d u / π 
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$-1/ \pi \int\limits^2_0 {e ^{u} } \, du =- \frac{e ^{- \pi x} }{ \pi } = \\ -1/ \pi (e ^{-2 \pi } -1) = \\ = \frac{1}{ \pi } - \frac{1}{ \pi e ^{2 \pi } }$