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?
$$(1-e^x)\int u^{10} du$$

let $x=\ln(u)$
$dx=du/u$
$I=\int e^{x}(1-e^x)(1+e^x)^{10} dx$ = $\int ((u(1-u)(1+u)^{10})/u)du$=$\int (1-u)(1+u)^{10}du$ 
You may want to take it from here...
