TeX Quellcode:

\begin{array}{rcl} \displaystyle\int \limits_1^3 \left(\sin(u)+3x^2-e^{-3t}+\dfrac{1}{x}\right) \, dx &=& 3 \displaystyle\int\limits_1^3 x^2 \, dx + \displaystyle\int\limits_1^3 \dfrac{1}{x} \, dx + \sin(u)\displaystyle\int\limits_1^3 1 \, dx-e^{-3t} \displaystyle\int\limits_1^3 1 \, dx \cr\cr&=& \left[x^3 + \ln(\left|x\right|) + \sin(u) \cdot x - e^{-3t}x\right]_1^3 \cr\cr &=& \left(3^3 + \ln(3) + \sin(u) \cdot 3 -e^{-3t} \cdot 3\right) - \left(1 + \ln(1) + \sin(u)-e^{-3t}\right) \cr\cr &=& 26+\ln\left(3\right)+2\sin\left(u\right)-2 e^{-3t} \end{array}