$\displaystyle \int_0^{10}(\frac{300x}{1+e^x})dx$
As I said there is no closed form expression. You cannot get an exact value of it.
$\displaystyle \int \frac{x}{1 + e^x}~dx = \frac{x^2}{2} - ln(1 + e^x) - \sum_{n = 1}^{\infty} \frac{e^{nx}}{n^2}$
There is no expression for that summation in terms of elementary functions. This thing can only be approximated.
-Dan
Edit: A made a mistake in copying "polylog" function from the Integrator site. I have fixed it.