TeX Quellcode:

\begin{array}{rclll} \dfrac{du}{dx} &=& -\sin(x) \cr dx &=& \dfrac{-1}{\sin(x)} \,du \cr\cr\cr \displaystyle\int \limits_0^{\frac{\pi}{4}} \dfrac{\sin(x)}{\cos(x)} \, dx &=& \displaystyle\int \limits_0^{\frac{\pi}{4}} \dfrac{\sin(x)}{u} \cdot \dfrac{-1}{\sin(x)} \, du \cr\cr&=& -1 \displaystyle\int \limits_0^{\frac{\pi}{4}} \dfrac{1}{u} \, du \cr &=& -1 \cdot \left[\ln(\vert u\vert)\right]_0^{\frac{\pi}{4}} \end{array}