TeX Quellcode:

\begin{array}{lrclcl} & \mathbb{D} &=& \mathbb{R} \cr\cr & 0 &=& 2x\left(2x^2e^{x^3+1}-9exe^{x^3}-5e^{x^3+1}\right) \cr & 0 &=& 4x^3e^{x^3+1}-18x^2e^{x^3+1}-10xe^{x^3+1} \cr & 0 &=& e^{x^3+1}\left(4x^3-18x^2-10x\right) &\vert& \text{Satz vom Nullprodukt} \cr \text{Faktor 1:} & 0 &=& e^{x^3+1} \cr\cr \text{Faktor 2:} & 0 &=& 4x^3-18x^2-10x \cr & 0 &=& x\left(4x^2-18x-10\right) &\vert& \text{Satz vom Nullprodukt} \cr \text{Faktor 2.1:} & 0 &=& x_1 \cr\cr \text{Faktor 2.2:} & 0 &=& 4x^2-18x-10 &\vert& :4 \cr & 0 &=& x^2-\dfrac{9}{2}x-\dfrac{5}{2} &\vert& \text{p-q-Formel} \cr\cr & x_{2,3} &=& \dfrac{9}{4} \pm \sqrt{\left(-\dfrac{9}{4}\right)^2+\dfrac{5}{2}} \cr & &=& \dfrac{9}{4} \pm \sqrt{\dfrac{121}{16}} \cr\cr & x_2 &=& \dfrac{9}{4} + \dfrac{11}{4} = 5 \cr\cr & x_3 &=& \dfrac{9}{4} - \dfrac{11}{4} = -\dfrac{1}{2} \end{array}