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Popular >

integral of a^xe^x

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

What is the integral of a^xe^x ?
The integral of a^xe^x is ((ae)^x)/(ln(ae))+C