I have an equation i wish to integrate
$\displaystyle
\int\frac{dx}{coshx+1}
$
What is the best way to start a problem like this. Should i substitute or integrate by parts? Any help appreciated!!
Try using its e identity.
$\displaystyle cosh(x)=\frac{1}{2}\left(e^{x}+e^{-x}\right)$
$\displaystyle \frac{1}{\frac{1}{2}\left(e^{x}+e^{-x}\right)+1}=$
$\displaystyle \frac{2e^{x}}{e^{2x}+2e^{x}+1}=\frac{2}{e^{x}+1}-\frac{2}{(e^{x}+1)^{2}}$
$\displaystyle 2\int\frac{1}{e^{x}+1}dx-2\int\frac{1}{(e^{x}+1)^{2}}dx$