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Beliebt Rechnen >

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

Lösung

\int e^{x^{2}} 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

integral from 0 to 4 of 2pi(2-y)(4y^2)

\int_{0}^{4} 2 π (2 - y) (4 y^{2}) d y

derivative (e^x)/(e^x+1)

d er i v a t i v e \frac{e ^{x}}{e ^{x} + 1}

y^{''}+5y=-180x^2e^{5x}

y^{^{''}} + 5 y = - 180 x^{2} e^{5 x}

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\int sin (m x) d x

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