integral of xe^{x/4}

Lösung

\int x e^{\frac{x}{4}} d x

4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}} + C

Schritte zur Lösung

\int x e^{\frac{x}{4}} d x

Wende die partielle Integration an

= 4 e^{\frac{x}{4}} x - \int 4 e^{\frac{x}{4}} d x

\int 4 e^{\frac{x}{4}} d x = 16 e^{\frac{x}{4}}

= 4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}}

Füge eine Konstante zur Lösung hinzu

= 4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}} + C

\int \frac{3 x ^{2}}{4 x - x ^{2}} d x

\frac{d y}{d x} = sin (3 x)

\frac{d y}{d x} = e^{3 x} + 8 y

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

\int \frac{( 8 x ^{2} + 3 x - 6 )}{( x ^{2} - 4 ) ( x + 2 )} d x