partielle-integration-smü

${\int }_{-1}^2(1+2t)\ast e^{2t}dt$ $u=2t$ $\frac{du}{dx}=2$ $dt=\frac{1}{2}du$ $\int (1+2t)\ast e^{2t}dt=\frac{1}{2}\ast \int (1+u)\ast e^u=\frac{1}{2}\ast \left((1+u)\ast e^u-\int e^{u}du\right)=\frac{1}{2}((1+u)\ast e^u-e^u)=\frac{1}{2}(1\ast 2t)\ast e^2-\frac{1}{2}{e}^{2t}$ ${\int }_{-1}^{-2}(1+2t)\ast e^{2t}dt=\frac{1}{2}\ast (1+2\ast 2)\ast e^{2\ast 2}-\frac{1}{2}(1+2)\ast (-1)\ast e^{2\ast (-1)}+\frac{1}{2}\ast e^{2\ast (-1)}$