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Beliebt Rechnen >

integral of e^{sqrt(5x)}

Lösung

\int e^{5 x} d x

Lösung

\frac{2}{5} e^{5 x} x - \frac{2}{5} e^{5 x} + C

Schritte zur Lösung

\int e^{5 x} d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

= \frac{2}{5} e^{5 x} x - \frac{2}{5} e^{5 x}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} e^{5 x} x - \frac{2}{5} e^{5 x} + C

Graph

Beliebte Beispiele

integral of (x^2)/(sqrt(x)+1)

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

integral of (x^2-1)sqrt(2x+1)

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derivative of 15x^2-15x^4

\frac{d}{d x} (15 x^{2} - 15 x^{4})

integral of 1/((x-6)^2)

\int \frac{1}{( x - 6 ) ^{2}} d x

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