TeX Quellcode:

\begin{array}{rcl} \displaystyle\int\limits_1^4 \left(x^3-6x^2+11x-2\right)\,dx &=& \displaystyle\int\limits_1^4 x^3 \, dx +\displaystyle\int\limits_1^4 -6x^2\,dx+\displaystyle\int\limits_1^4 11x\, dx +\displaystyle\int\limits_1^4 -2\,dx \cr\cr &=& \displaystyle\int\limits_1^4 x^3 \, dx -6\displaystyle\int\limits_1^4 x^2\,dx+11\displaystyle\int\limits_1^4 x\, dx -2\displaystyle\int\limits_1^4 1\,dx \cr\cr &=& \left[\dfrac{1}{4}x^4-6\cdot\dfrac{1}{3}x^3+11\cdot\dfrac{1}{2}x^2-2x\right]_1^4\cr\cr &=& \left[\dfrac{1}{4}x^4-2x^3+\dfrac{11}{2}x^2-2x\right]_1^4 \cr\cr &=& \dfrac{1}{4}\cdot4^4-2\cdot4^3+\dfrac{11}{2}\cdot4^2-2\cdot4-\left(\dfrac{1}{4}-2+\dfrac{11}{2}-2\right) \cr\cr &=& \dfrac{57}{4} \end{array}