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Popular Calculus >

integral of e^xa^x

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

e^{x} a^{x} = (e a)^{x}

= \int (e a)^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

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

Add a constant to the solution

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

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

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