What is the integral of e^{5x}+a^{5x} ?

The integral of e^{5x}+a^{5x} is 1/5 e^{5x}+(a^{5x})/(5ln(a))+C

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

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

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

Solution steps

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

Apply the Sum Rule:

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

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

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

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

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

Add a constant to the solution

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

\int sec (x) (5 sec (x) + 2 tan (x)) d x

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

\int e^{x} - 1 d x

What is the integral of e^{5x}+a^{5x} ?
The integral of e^{5x}+a^{5x} is 1/5 e^{5x}+(a^{5x})/(5ln(a))+C