Evaluating Integral $\int e^{x}(1-e^x)(1+e^x)^{10} dx$ I have this integral to evaluate: $$\int e^{x}(1-e^x)(1+e^x)^{10} dx$$
I figured to use u substitution for the part that is raised to the tenth power. After doing this the $e^x$ is canceled out.
I am not sure where to go from here however due to the $(1-e^x)$. 
Is it possible to move it to the outside like this and continue from here with evaluating the integral?
$$(1-e^x)\int u^{10} du$$

FWIFs, this also would be easily generalized via a recurrence relation (aside from the obvious substitution that confirms this] as the integral is of the form;
f ' (x) times g(x) (where f(x) is (1/11)(1+e^x)^11) and f(x), g(x) both behave good enough - i.e. we get back something close enough to our integral the define a recurrence.
