Question

Integrate [(e^(x) + e^(-x) )/(e^x - e^(-x)]

Answer 1

\[\large \int\limits\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}} dx\]
let u = \(e^x+e^-x\) => \(\frac{du}{e^{x}+e^{-x}} \)

Answer 2

Can you work it out more?

Answer 3

\[\large \int\limits\frac{e^{x}+e^{-x}}{u} *\frac{du}{e^{x}+e^{-x}} => \int\limits\frac{1}{u} => \ln(u) + C =>\]
\[\large \ln(e^x-e^-x) +c\]

Answer 4

woops, typo:
\[\ln(e ^{x} -e ^{-x}) +c\]

Answer 5

Thank you ^^