Question

Evaulate.....

Answer 1

\[\int\limits_{-\infty}^{\infty}\frac{ 1 }{ e ^{x}+e ^{-x} }dx\]please show how you got the answer

Answer 2

It should be usefull,
\[\int\frac{1}{1+x^2}dx=\arctan x\]
Then,
\[\int_{-\infty}^{\infty}\frac{1}{e^x+e^{-x}}dx=\int_{-\infty}^{\infty}\frac{e^x}{1+(e^{x})^2}dx=\arctan(e^{\infty})-\arctan(e^{-\infty})=\pi/2\]
Also, you can substitute the infinities by the epsilon formalism for improper integrals, ans use limits, the result will be the same.

Answer 3

Great Thanks

Answer 4

You're welcome.