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Beliebt Rechnen >

integral of (1+e^{2x})/(e^x)

Lösung

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

Lösung

- \frac{1}{e ^{x}} + e^{x} + C

Schritte zur Lösung

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

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

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= - \frac{1}{e ^{x}} + e^{x}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{e ^{x}} + e^{x} + C

Graph

Beliebte Beispiele

integral of 9/(x+2)

\int \frac{9}{x + 2} d x

limit as x approaches 4-of 3/(x-4)

x \to 4 - lim (\frac{3}{x - 4})

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d er i v a t i v e \frac{4 x}{x ^{2} + 6}

integral of 9sin^2(x)cos^3(x)

\int 9 sin^{2} (x) cos^{3} (x) d x

limit as x approaches 1-of xln(x)

x \to 1 - lim (x ln (x))