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Beliebt Rechnen >

integral of e^{sqrt(x)}x

Lösung

\int e^{x} x d x

Lösung

2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x}))) + C

Schritte zur Lösung

\int e^{x} x d x

Wende U-Substitution an

= \int 2 e^{u} u^{3} d u

Entferne die Konstante:

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

= 2 \cdot \int e^{u} u^{3} d u

Wende die partielle Integration an

= 2 (u^{3} e^{u} - \int 3 u^{2} e^{u} d u)

\int 3 u^{2} e^{u} d u = 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u}))

= 2 (u^{3} e^{u} - 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u})))

Setze in

u = x

ein

= 2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x})))

Vereinfache

2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x}))) : 2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

= 2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

Füge eine Konstante zur Lösung hinzu

= 2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x}))) + C

Graph

Beliebte Beispiele

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