Answer
$\frac{{{e^x}}}{{1 + {e^{2a}}}} + C$
Work Step by Step
$$\eqalign{
& \int {\frac{{{e^x}}}{{1 + {e^{2a}}}}} dx \cr
& \int {\frac{{{e^x}}}{{1 + {e^{2a}}}}} dx = \int {\left( {\frac{1}{{1 + {e^{2a}}}}} \right){e^x}} dx \cr
& {\text{Pull out the constant }}\frac{1}{{1 + {e^{2a}}}} \cr
& = \frac{1}{{1 + {e^{2a}}}}\int {{e^x}} dx \cr
& {\text{Integrate}} \cr
& = \frac{1}{{1 + {e^{2a}}}}\left( {{e^x}} \right) + C \cr
& = \frac{{{e^x}}}{{1 + {e^{2a}}}} + C \cr} $$
