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Popular Calculus >

integral of e^xe^x

Solution

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

Solution

\frac{1}{2} e^{2 x} + C

Solution steps

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

Apply exponent rule:

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

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

= \int (ee)^{x} d x

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

= \frac{( ee ) ^{x}}{ln ( ee )}

Simplify

\frac{( ee ) ^{x}}{ln ( ee )} : \frac{1}{2} e^{2 x}

= \frac{1}{2} e^{2 x}

Add a constant to the solution

= \frac{1}{2} e^{2 x} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of e^xe^x ?
The integral of e^xe^x is 1/2 e^{2x}+C