de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of xe^{-2/5 x}

Lösung

\int x e^{- \frac{2}{5} x} d x

Lösung

- \frac{5}{2} e^{- \frac{2 x}{5}} x - \frac{25}{4} e^{- \frac{2 x}{5}} + C

Schritte zur Lösung

\int x e^{- \frac{2}{5} x} d x

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \int x e^{- \frac{2 x}{5}} d x

Wende die partielle Integration an

= \frac{1}{2} e^{- \frac{2 x}{5}} x^{2} - \int - \frac{1}{5} e^{- \frac{2 x}{5}} x^{2} d x

\int - \frac{1}{5} e^{- \frac{2 x}{5}} x^{2} d x = \frac{1}{4} (2 e^{- \frac{2 x}{5}} x^{2} - 25 (- \frac{2 e ^{- \frac{2 x}{5}} x}{5} - e^{- \frac{2 x}{5}}))

= \frac{1}{2} e^{- \frac{2 x}{5}} x^{2} - \frac{1}{4} (2 e^{- \frac{2 x}{5}} x^{2} - 25 (- \frac{2 e ^{- \frac{2 x}{5}} x}{5} - e^{- \frac{2 x}{5}}))

Vereinfache

\frac{1}{2} e^{- \frac{2 x}{5}} x^{2} - \frac{1}{4} (2 e^{- \frac{2 x}{5}} x^{2} - 25 (- \frac{2 e ^{- \frac{2 x}{5}} x}{5} - e^{- \frac{2 x}{5}})) : - \frac{5}{2} e^{- \frac{2 x}{5}} x - \frac{25}{4} e^{- \frac{2 x}{5}}

= - \frac{5}{2} e^{- \frac{2 x}{5}} x - \frac{25}{4} e^{- \frac{2 x}{5}}

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{2} e^{- \frac{2 x}{5}} x - \frac{25}{4} e^{- \frac{2 x}{5}} + C

Graph

Beliebte Beispiele

(dy)/(dx)=\sqrt[3]{x}

\frac{d y}{d x} = 3 x

integral of 1/((x-1)(x^2+1))

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

y^{''}-5y^'-6y=12e^2t

y^{^{''}} - 5 y^{^{'}} - 6 y = 12 e^{2} t

(\partial)/(\partial x)(ye^{3x})

\frac{\partial}{\partial x} (y e^{3 x})

derivative of-2(2x^2-4x-1^2)

\frac{d}{d x} (- 2 (2 x^{2} - 4 x - 1)^{2})