Analytical integration of product of exponential functions

Question

I am trying to obtain an analytical formula for the following integral. My first question is whether it is possible to obtain an analytical formula without the use of transcendental functions. My second question is to ask whether anybody has any idea how to calculate this integral. Many thanks for any pointers you may have. $$ \int_{0}^{t}{\left\{ \sum\limits_{i=0}^{mMax}{{{A}_{i}}\,}{{e}^{-\xi /{{B}_{i}}}}\left[ \frac{\text{ }{{\text{e}}^{-2k\left( -\xi -T/2 \right)}}}{{{\left( 1+{{\text{e}}^{-2k\left( -\xi -T/2 \right)}} \right)}^{2}}}-\underset{n=1}{\overset{nMax}{\mathop \sum }}\,2{{\left( -1 \right)}^{n}}\frac{\,{{\text{e}}^{-2k\left( \xi -nT \right)}}}{{{\left( 1+{{\text{e}}^{-2k\left( \xi -nT \right)}} \right)}^{2}}} \right] \right\}\,d\xi } $$