integral of (a^{5x}+e^{5x})

Lösung

\int (a^{5 x} + e^{5 x}) d x

\frac{a ^{5 x}}{5 ln ( a )} + \frac{1}{5} e^{5 x} + C

Schritte zur Lösung

\int a^{5 x} + e^{5 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 a^{5 x} d x + \int e^{5 x} d x

\int a^{5 x} d x = \frac{a ^{5 x}}{5 ln ( a )}

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

= \frac{a ^{5 x}}{5 ln ( a )} + \frac{1}{5} e^{5 x}

Füge eine Konstante zur Lösung hinzu

= \frac{a ^{5 x}}{5 ln ( a )} + \frac{1}{5} e^{5 x} + C

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