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Beliebt Rechnen >

integral of x^2*e^{5x}

Lösung

\int x^{2} \cdot e^{5 x} d x

Lösung

\frac{1}{5} e^{5 x} x^{2} - \frac{2}{125} (5 e^{5 x} x - e^{5 x}) + C

Schritte zur Lösung

\int x^{2} e^{5 x} d x

Wende die partielle Integration an

= \frac{1}{5} e^{5 x} x^{2} - \int \frac{2}{5} e^{5 x} x d x

\int \frac{2}{5} e^{5 x} x d x = \frac{2}{125} (5 e^{5 x} x - e^{5 x})

= \frac{1}{5} e^{5 x} x^{2} - \frac{2}{125} (5 e^{5 x} x - e^{5 x})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} e^{5 x} x^{2} - \frac{2}{125} (5 e^{5 x} x - e^{5 x}) + C

Graph

Beliebte Beispiele

sum from n=-1 to infinity of (1/2)^n

integral from-infinity to 0 of 1/(7-10x)

derivative of 2x^2+3x-5

integral of (x^3)/3 (1/x)

integral of (2x^5)/(3x^2+4)