Vi använder samma teknik som i videon för att skriva om integralen som \[ I=\int_{0}^{\frac{\pi}{2}}\left(\int_{0}^{1}\left(\int_{0}^{1} x^2y\cos(xyz)\,dz\right)dy\right)dx= \] \[ \int_{0}^{\frac{\pi}{2}}\left(\int_{0}^{1}\Big[x\sin(xyz)\Big]_{0}^{1}dy\right)dx= \int_{0}^{\frac{\pi}{2}}\left(\int_{0}^{1}x\sin (xy)\,dy\right)dx= \] \[ \int_{0}^{\frac{\pi}{2}}\Big[-\cos(xy)\Big]_{0}^{1}dx= \int_{0}^{\frac{\pi}{2}}\left(1-\cos x\right)\,dx= \] \[ \Big[x-\sin x\Big]_{0}^{\frac{\pi}{2}}=\frac{\pi}{2}-1. \]