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Beliebt Rechnen >

integral of 5xe^{x/5}

Lösung

\int 5 x e^{\frac{x}{5}} d x

Lösung

5 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}}) + C

Schritte zur Lösung

\int 5 x e^{\frac{x}{5}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x e^{\frac{x}{5}} d x

Wende die partielle Integration an

= 5 (5 e^{\frac{x}{5}} x - \int 5 e^{\frac{x}{5}} d x)

\int 5 e^{\frac{x}{5}} d x = 25 e^{\frac{x}{5}}

= 5 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}})

Füge eine Konstante zur Lösung hinzu

= 5 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}}) + C

Graph

Beliebte Beispiele

integral of (sec^2(x)+3)

\int (sec^{2} (x) + 3) d x

\int e x d x

y^{''}+4y^'+4y=0

y^{^{''}} + 4 y^{^{'}} + 4 y = 0

derivative of (24/((1-x)^5))

\frac{d}{d x} (\frac{24}{( 1 - x ) ^{5}})

derivative (ln|x+2|)^7

d er i v a t i v e (ln ∣ x + 2 ∣)^{7}