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Beliebt Rechnen >

integral of 1/(\sqrt[5]{x)}+5/(e^{3x)}

Lösung

\int \frac{1}{5 x} + \frac{5}{e ^{3 x}} d x

Lösung

\frac{5}{4} x^{\frac{4}{5}} - \frac{5}{3} e^{- 3 x} + C

Schritte zur Lösung

\int \frac{1}{5 x} + \frac{5}{e ^{3 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}{5 x} d x + \int \frac{5}{e ^{3 x}} d x

\int \frac{1}{5 x} d x = \frac{5}{4} x^{\frac{4}{5}}

\int \frac{5}{e ^{3 x}} d x = - \frac{5}{3} e^{- 3 x}

= \frac{5}{4} x^{\frac{4}{5}} - \frac{5}{3} e^{- 3 x}

Füge eine Konstante zur Lösung hinzu

= \frac{5}{4} x^{\frac{4}{5}} - \frac{5}{3} e^{- 3 x} + C

Graph

Beliebte Beispiele

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