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Beliebt Rechnen >

integral of e^{sqrt(x)}sqrt(x)

Lösung

\int e^{x} x d x

Lösung

2 (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^{2} 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^{2} d u

Wende die partielle Integration an

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

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

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

Setze in

u = x

ein

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

(x)^{2} = x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of sqrt(1+2x^2)

\int 1 + 2 x^{2} d x

integral of (x-2)/(x^2-10x+106)

\int \frac{x - 2}{x ^{2} - 10 x + 106} d x

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\int sec (2 y) tan (2 y) d y

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\int 9 (x^{2} + 3 x + 5) (2 x + 3) d x

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\int \frac{ln ^{2} ( x )}{x ^{5}} d x