integral of integral of e^{x/y}

Lösung

\int \int e^{\frac{x}{y}} d x d y

C y + \frac{1}{2} e^{\frac{x}{y}} y^{2} + \frac{x e ^{\frac{x}{y}} y}{2} - x \frac{x}{2} Ei (\frac{x}{y}) + C

Schritte zur Lösung

\int \int e^{\frac{x}{y}} d x d y

\int e^{\frac{x}{y}} d x = y e^{\frac{x}{y}} + C

= \int (y e^{\frac{x}{y}} + C) d y

\int (y e^{\frac{x}{y}} + C) d y = C y + \frac{1}{2} e^{\frac{x}{y}} y^{2} + \frac{x e ^{\frac{x}{y}} y}{2} - x \frac{x}{2} Ei (\frac{x}{y}) + C

= C y + \frac{1}{2} e^{\frac{x}{y}} y^{2} + \frac{x e ^{\frac{x}{y}} y}{2} - x \frac{x}{2} Ei (\frac{x}{y}) + C

\int \int x cos (y) d A

\int \int \frac{1}{2}

\int_{0}^{1} \int_{0}^{1} 17 + 4 z^{2} d x d z

\int \int y d y d y

x \to 3 + lim (ln (\frac{1}{x - 3}))