TeX Quellcode:

\begin{array}{rcl}\displaystyle\int (8x^3-9x^2)\sin(5x)\,dx &=& -\dfrac{1}{5}\left(8x^3-9x^2\right)\cos(5x)+\dfrac{1}{5}\left(\dfrac{1}{5} \left(24x^2-18x\right)\sin(5x)-\dfrac{1}{5}\left(-\dfrac{1}{5}\left(48x-18\right)\cos(5x)+\dfrac{48}{25}\sin(5x)+ c \right)\right) \cr\cr &=& -\dfrac{1}{5}\left(8x^3-9x^2\right)\cos(5x)+\dfrac{1}{5}\left(\dfrac{1}{5}\left(24x^2-18x\right)\sin(5x)+\dfrac{1}{25}\left(48x-18\right)\cos(5x) -\dfrac{48}{125}\sin(5x)+ c \right) \cr\cr &=& -\dfrac{1}{5}\left(8x^3-9x^2\right)\cos(5x)+\dfrac{1}{25}\left(24x^2-18x\right)\sin(5x)+\dfrac{1}{125}\left(48x-18\right)\cos(5x) -\dfrac{48}{625}\sin(5x)+ c \cr\cr &=& \dfrac{1}{25}\left(24x^2-18x\right)\sin(5x)-\dfrac{48}{625}\sin(5x)-\dfrac{1}{5}\left(8x^3-9x^2\right)\cos(5x)+\dfrac{1}{125}\left(48x-18\right)\cos(5x)+ c \cr\cr &=& \dfrac{1}{25}\sin(5x)\left(24x^2-18x-\dfrac{48}{25}\right)+\dfrac{1}{5}\cos(5x)\left(-8x^3+9x^2+\dfrac{1}{25}\left(48x-18\right)\right)+ c \end{array}