Integration and evaluation I have to evaluate this integral here 
$$\int_x^\infty \frac{1}{1+e^t} dt$$
I've tried with the substitution $e^t=k$, but at the end I get $\log|k|-\log|1+k| $, which evaluated between the extrema doesn't converge... I hope that somebody can help!

Hint:
$$\frac { 1 }{ 1+{ e }^{ t } } =\frac { 1 }{ { e }^{ t }\left( 1+{ e }^{ -t } \right)  } =\frac { { e }^{ -t } }{ 1+{ e }^{ -t } } \\ \int { \frac { dt }{ 1+{ e }^{ t } }  } =-\int { \frac { d\left( 1+{ e }^{ -t } \right)  }{ 1+{ e }^{ -t } }  } $$
