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Beliebt Rechnen >

integral of (ye^{xy}+y/(x^2))

Lösung

\int (y e^{x y} + \frac{y}{x ^{2}}) d x

Lösung

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 1/(x^5sqrt(ln(x)))

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

integral of (1+e^{-2y})^{1/4}e^{-2y}

\int (1 + e^{- 2 y})^{\frac{1}{4}} e^{- 2 y} d y

integral of 1/((x+1)(x-5))

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

integral of (e^{xy})/(y^2)

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

integral of (12x^2)

\int (12 x^{2}) d x