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

Lösung

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

- \frac{1}{2} e^{- 2 x} - \frac{2}{e ^{x}} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{1 + 2 e ^{x}}{e ^{2 x}} : \frac{1}{e ^{2 x}} + \frac{2}{e ^{x}}

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

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

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

= - \frac{1}{2} e^{- 2 x} - \frac{2}{e ^{x}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} e^{- 2 x} - \frac{2}{e ^{x}} + C

in t e g r a l x^{7}

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