What is the integral of (e^xe^x)/(-2) ?

The integral of (e^xe^x)/(-2) is -1/4 e^{2x}+C

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integral of (e^xe^x)/(-2)

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

- \frac{1}{4} e^{2 x} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{- 2} \cdot \int e^{x} e^{x} d x

Simplify

= (- \frac{1}{2}) \cdot \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}

= (- \frac{1}{2}) \cdot \int (ee)^{x} d x

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

= (- \frac{1}{2}) \frac{( ee ) ^{x}}{ln ( ee )}

Simplify

(- \frac{1}{2}) \frac{( ee ) ^{x}}{ln ( ee )} : - \frac{1}{4} e^{2 x}

= - \frac{1}{4} e^{2 x}

Add a constant to the solution

= - \frac{1}{4} e^{2 x} + C

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What is the integral of (e^xe^x)/(-2) ?
The integral of (e^xe^x)/(-2) is -1/4 e^{2x}+C