Question

How to integrate e^(-2x)/(1+e^(-x)) dx?

Answer 1

\[\int\limits_{}^{}\frac{ e ^{-2x} }{ 1+e ^{-x} } dx\]

Answer 2

@ganeshie8 @jabez177 @inkyvoyd @Conqueror @mathmath333

Answer 3

i'd go \(u = e^{-x}, du = - e^{-x} dx = -u ~dx \)


that already looks promising

so \(\int ~ \dfrac{u^2}{1 + u } . \dfrac{-1}{u} ~ du\)

\(= - \int ~ \dfrac{u}{1 + u } ~ du\)

\(=- \int ~ \dfrac{1 + u - 1}{1 + u } ~ du\)


\(=- \int ~ 1 - \dfrac{ 1}{1 + u } ~ du\)

bish bosh