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Beliebt Rechnen >

integral of x^2e^{8x}

Lösung

\int x^{2} e^{8 x} d x

Lösung

\frac{1}{8} e^{8 x} x^{2} - \frac{1}{256} (8 e^{8 x} x - e^{8 x}) + C

Schritte zur Lösung

\int x^{2} e^{8 x} d x

Wende die partielle Integration an

= \frac{1}{8} e^{8 x} x^{2} - \int \frac{1}{4} e^{8 x} x d x

\int \frac{1}{4} e^{8 x} x d x = \frac{1}{256} (8 e^{8 x} x - e^{8 x})

= \frac{1}{8} e^{8 x} x^{2} - \frac{1}{256} (8 e^{8 x} x - e^{8 x})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{8} e^{8 x} x^{2} - \frac{1}{256} (8 e^{8 x} x - e^{8 x}) + C

Graph

Beliebte Beispiele

integral from 0 to 6 of 1/(x^2-36)

\int_{0}^{6} \frac{1}{x ^{2} - 36} d x

integral of e^xx-e^x

\int e^{x} x - e^{x} d x

limit as x approaches 5 of x^3

x \to 5 lim (x^{3})

integral of 1/(x^2-2x+5)

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

y^{''}-y^'-2y=7e^{-t}

y^{^{''}} - y^{^{'}} - 2 y = 7 e^{- t}