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Popular >

integral of 5^xe^x

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

5^{x} e^{x} = (5 e)^{x}

= \int (5 e)^{x} d x

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

What is the integral of 5^xe^x ?
The integral of 5^xe^x is ((5e)^x)/(ln(5e))+C