What is the integral of (e^x-15^x) ?

The integral of (e^x-15^x) is e^x-(15^x)/(ln(15))+C

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integral of (e^x-15^x)

\int (e^{x} - 1 5^{x}) d x

e^{x} - \frac{1 5 ^{x}}{ln ( 15 )} + C

Solution steps

\int e^{x} - 1 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^{x} d x - \int 1 5^{x} d x

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

\int 1 5^{x} d x = \frac{1 5 ^{x}}{ln ( 15 )}

= e^{x} - \frac{1 5 ^{x}}{ln ( 15 )}

Add a constant to the solution

= e^{x} - \frac{1 5 ^{x}}{ln ( 15 )} + C

\frac{\partial}{\partial x} (x^{3} + x^{2} y)

\int \frac{cos ( 3 x )}{1 + sin ^{2} ( 3 x )} d x

x \to 0 lim (tan (2 x))

\frac{d}{d x} (3 x + 9)

\frac{\partial}{\partial y} (e^{a x + y} + e^{y})

What is the integral of (e^x-15^x) ?
The integral of (e^x-15^x) is e^x-(15^x)/(ln(15))+C