# Math Help - e^x integral

1. ## e^x integral

$\int\frac{e^{3x}}{e^x+e^{-x}}$

can you do this with substitution somehow?

2. $\int {\frac{{e^{3x} }}
{{e^x + e^{ - x} }}\,dx} = \int {\frac{{e^{4x} }}
{{e^{2x} + 1}}\,dx} .$

Now this is routine, substitute $u=e^{2x},$

$\int {\frac{{e^{3x} }}
{{e^x + e^{ - x} }}\,dx} = \frac{1}
{2}\int {\frac{u}
{{u + 1}}\,du} = \frac{1}
{2}\left( {\int {du} - \int {\frac{1}
{{u + 1}}\,du} } \right).$

From here the rest is quite straightforward.