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Popular Calculus >

integral of 2^x*e^x

Solution

\int 2^{x} \cdot e^{x} d x

Solution

\frac{( 2 e ) ^{x}}{ln ( 2 e )} + C

Solution steps

\int 2^{x} e^{x} d x

Apply exponent rule:

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

2^{x} e^{x} = (2 e)^{x}

= \int (2 e)^{x} d x

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

= \frac{( 2 e ) ^{x}}{ln ( 2 e )}

Add a constant to the solution

= \frac{( 2 e ) ^{x}}{ln ( 2 e )} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 2^x*e^x ?
The integral of 2^x*e^x is ((2e)^x)/(ln(2e))+C