Aus Online Mathematik Brückenkurs 2

If we multiply the factors in the integrand together and use the power laws,

\displaystyle \begin{align} & \int{e^{2x}}\left( e^{x}+1 \right)\,dx=\int{\left( e^{2x}e^{x}+e^{2x} \right)}\,dx \\ & =\int{\left( e^{2x+x}+e^{2x} \right)}\,dx=\int{\left( e^{3x}+e^{2x} \right)}\,dx \\ \end{align}

we obtain a standard integral with two terms of the type \displaystyle e^{ax}, where \displaystyle a is a constant. The indefinite integral is therefore

\displaystyle \int{\left( e^{3x}+e^{2x} \right)}\,dx=\frac{e^{3x}}{3}+\frac{e^{2x}}{2}+C

where \displaystyle C is an arbitrary constant.