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

f (x) = \frac{- 1}{x ^{2}}

\int \frac{x e ^{4 x}}{( 4 x + 1 ) ^{2}} d x

4 \cdot ln (x)

\int tan^{3} (x) d x

\frac{\partial}{\partial x} (10 arctan (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