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Popular Calculus >

integral of 3xe^2x

Solution

\int 3 x e^{2} x d x

Solution

e^{2} x^{3} + C

Solution steps

\int 3 x e^{2} x d x

Take the constant out:

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

= 3 e^{2} \cdot \int xx d x

Simplify

xx : x^{2}

= 3 e^{2} \cdot \int x^{2} d x

Apply the Power Rule

= 3 e^{2} \frac{x ^{3}}{3}

Simplify

3 e^{2} \frac{x ^{3}}{3} : e^{2} x^{3}

= e^{2} x^{3}

Add a constant to the solution

= e^{2} x^{3} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 3xe^2x ?
The integral of 3xe^2x is e^2x^3+C