Question Number 67708 by aliesam last updated on 30/Aug/19
Answered by mind is power last updated on 30/Aug/19
![z=(x/y) y=(x/z) dy=−(x/z^2 )dz ∫−((xe^z )/z^2 )dz=x∫−(e^z /z^2 )dz=x[(e^z /z)−∫(e^z /z)dz] =((xe^z )/z)−x∫(e^z /z)dz =((xe^z )/z)−xE(z) E(z)=exponontiel integral](Q67729.png)
$${z}=\frac{{x}}{{y}} \\ $$$${y}=\frac{{x}}{{z}} \\ $$$${dy}=−\frac{{x}}{{z}^{\mathrm{2}} }{dz} \\ $$$$\int−\frac{{xe}^{{z}} }{{z}^{\mathrm{2}} }{dz}={x}\int−\frac{{e}^{{z}} }{{z}^{\mathrm{2}} }{dz}={x}\left[\frac{{e}^{{z}} }{{z}}−\int\frac{{e}^{{z}} }{{z}}{dz}\right] \\ $$$$=\frac{{xe}^{{z}} }{{z}}−{x}\int\frac{{e}^{{z}} }{{z}}{dz} \\ $$$$=\frac{{xe}^{{z}} }{{z}}−{xE}\left({z}\right) \\ $$$${E}\left({z}\right)={exponontiel}\:{integral} \\ $$