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Beliebt Rechnen >

integral of e^{x^2}*x^3

Lösung

\int e^{x^{2}} \cdot x^{3} d x

Lösung

\frac{1}{2} (e^{x^{2}} x^{2} - e^{x^{2}}) + C

Schritte zur Lösung

\int e^{x^{2}} x^{3} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int e^{u} u d u

Wende die partielle Integration an

= \frac{1}{2} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{2} (e^{u} u - e^{u})

Setze in

u = x^{2}

ein

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (e^{x^{2}} x^{2} - e^{x^{2}}) + C

Graph

Beliebte Beispiele

derivative of (x^2-3x+1^4)

\frac{d}{d x} ((x^{2} - 3 x + 1)^{4})

fläche 5x, 5/3 x,14-x^2

a re a 5 x, \frac{5}{3} x, 14 - x^{2}

derivative 9e^x

d er i v a t i v e 9 e^{x}

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d er i v a t i v e y (X) = \frac{1}{2 cos ^{2} ( X )}

limit as x approaches 0 of (3x^2-2)^5

x \to 0 lim ((3 x^{2} - 2)^{5})