What is the integral of e[2x] ?

The integral of e[2x] is ex^2+C

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integral of e[2x]

\int e [2 x] d x

e x^{2} + C

Solution steps

\int e [2 x] d x

Take the constant out:

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

= e \cdot \int 2 x d x

Take the constant out:

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

= e 2 \cdot \int x d x

Apply the Power Rule

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

Simplify

e 2 \cdot \frac{x ^{2}}{2} : e x^{2}

= e x^{2}

Add a constant to the solution

= e x^{2} + C