TeX Quellcode:

\begin{array}{rclcl} \displaystyle\int \limits_1^8 \dfrac{5(x-7)^2}{\left(25x^4-350x^3+1.225x^2\right)\sqrt[3]{x}} \, dx &=& \displaystyle\int \limits_1^8 \dfrac{5(x-7)^2}{25\left(x^4-14x^3+49x^2\right)\sqrt[3]{x}} \, dx \cr\cr&=& \displaystyle\int \limits_1^8 \dfrac{1}{5} \cdot \dfrac{(x-7)^2}{\left(x^4-14x^3+49x^2\right)\sqrt[3]{x}} \, dx \cr\cr&=& \dfrac{1}{5} \displaystyle\int \limits_1^8 \dfrac{(x-7)^2}{x^2\left(x^2-14x+49\right)\sqrt[3]{x}} \, dx \cr\cr&=& \dfrac{1}{5} \displaystyle\int \limits_1^8 \dfrac{(x-7)^2}{x^2\left(x-7\right)^2\sqrt[3]{x}} \, dx \cr\cr&=& \dfrac{1}{5} \displaystyle\int \limits_1^8 \dfrac{1}{x^2 \cdot x^{\frac{1}{3}}} \, dx \cr\cr&=& \dfrac{1}{5} \displaystyle\int \limits_1^8 x^{-\frac{7}{3}} \, dx \cr\cr&=& \dfrac{1}{5} \cdot \left[-\dfrac{3}{4x^{\frac{4}{3}}}\right]_1^8 \cr\cr&=& -\dfrac{3}{20} \cdot \left[\dfrac{1}{\sqrt[3]{x^4}}\right]_1^8 \cr\cr&=& -\dfrac{3}{20} \left(\dfrac{1}{\sqrt[3]{8^4}} - \dfrac{1}{\sqrt[3]{1^4}}\right) \cr\cr&=& \dfrac{9}{64} \end{array}