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Beliebt Rechnen >

integral of e^{5x}x^2

Lösung

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

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

\int \frac{4 x ^{2}}{x ^{3} + 4} d x

integral of t^2e^{-t}

\int t^{2} e^{- t} d t

limit as x approaches 2 of 1/(x^2-1)

x \to 2 lim (\frac{1}{x ^{2} - 1})

fläche y= 1/(8x^2),y=x,y= x/8

a re a y = \frac{1}{8 x ^{2}}, y = x, y = \frac{x}{8}

derivative of xsec(y)

\frac{d}{d x} (x sec (y))