integral of y-y/(x^2)e^{y/x}

Lösung

\int y - \frac{y}{x ^{2}} e^{\frac{y}{x}} d x

y x + e^{\frac{y}{x}} + C

Schritte zur Lösung

\int y - \frac{y}{x ^{2}} e^{\frac{y}{x}} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y d x - \int \frac{y}{x ^{2}} e^{\frac{y}{x}} d x

\int y d x = y x

\int \frac{y}{x ^{2}} e^{\frac{y}{x}} d x = - e^{\frac{y}{x}}

= y x - (- e^{\frac{y}{x}})

Vereinfache

= y x + e^{\frac{y}{x}}

Füge eine Konstante zur Lösung hinzu

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

f (x) = (tan (x))^{x}

y^{3} d x + 3 x y^{2} d y = 0

\int \frac{( 2 x ^{2} + 5 )}{x ^{2} + 1} d x

x \to \infty lim (x + 6)

\frac{\partial}{\partial x} (\frac{1}{2 x ^{\frac{5}{2} y^{\frac{1}{2}}}})