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Beliebt Rechnen >

integral of x^2e^{ax}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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d er i v a t i v e (4 x + cos (2))^{55}

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\int \frac{x}{10} d x

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\int_{0}^{\frac{π}{4}} cos^{2} (4 x) d x

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\int \frac{2 x + 1}{x ^{3} - 7 x + 6} d x

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