What is the integral of (e^{x/n}-a^{x/n}) ?

The integral of (e^{x/n}-a^{x/n}) is -(na^{x/n})/(ln(a))+ne^{x/n}+C

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integral of (e^{x/n}-a^{x/n})

\int (e^{\frac{x}{n}} - a^{\frac{x}{n}}) d x

- \frac{n a ^{\frac{x}{n}}}{ln ( a )} + n e^{\frac{x}{n}} + C

Solution steps

\int e^{\frac{x}{n}} - a^{\frac{x}{n}} 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 a^{\frac{x}{n}} d x + \int e^{\frac{x}{n}} d x

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

\int e^{\frac{x}{n}} d x = n e^{\frac{x}{n}}

= - \frac{n a ^{\frac{x}{n}}}{ln ( a )} + n e^{\frac{x}{n}}

Add a constant to the solution

= - \frac{n a ^{\frac{x}{n}}}{ln ( a )} + n e^{\frac{x}{n}} + C

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What is the integral of (e^{x/n}-a^{x/n}) ?
The integral of (e^{x/n}-a^{x/n}) is -(na^{x/n})/(ln(a))+ne^{x/n}+C