Question

Integrate w.r.t $x$ $e^x\left(\frac{1+\cos x}{1+\cos x}\right)$

Answer 1

$\int x{e}^x\left(\frac{1+\cos x}{1+\cos x}\right)dx$

$\Rightarrow \int x{e}^{x}dx$

Using ILATE rule, so $x$ will be first function & $e^x$ be second, then

$\Rightarrow x{e}^x-\int e^{x}dx$

$\Rightarrow x{e}^x-e^x=e^x(x-1)$