\(\qquad \displaystyle\int -\frac{1}{2}\cdot e^{4x-2}-1\, dx\) \(=-\dfrac{1}{8}\cdot e^{4x-2}-x+c\)

\(\qquad \displaystyle\int ex-e^{2-x}\, dx\) \(=\dfrac{e}{2}\cdot x^2+e^{2-x}+c\)

\(\qquad \displaystyle\int x^2-1+e^{-x}\, dx\) \(=\dfrac{1}{3}\cdot x^3-x- e^{-x}+c\)

Wir integrieren die Funktionen mithilfe der linearen Verkettung:

\(\qquad \displaystyle\int -\dfrac{1}{2}\cdot e^{4x-2}-1\, dx=-\dfrac{1}{2}\cdot \dfrac{1}{4}\cdot e^{4x-2}-x+c\) \(=-\dfrac{1}{8}\cdot e^{4x-2}-x+c\)

\(\qquad \displaystyle\int ex-e^{2-x}\, dx=e\cdot \dfrac{1}{2}\cdot x^2-(-1)\cdot e^{2-x}+c\) \(=\dfrac{e}{2}\cdot x^2+e^{2-x}+c\)

\(\qquad \displaystyle\int x^2-1+e^{-x}\, dx=\dfrac{1}{3}\cdot x^3-x+(-1)\cdot e^{-x}+c\) \(=\dfrac{1}{3}\cdot x^3-x- e^{-x}+c\)