What is the integral of x^2e^2x ?

The integral of x^2e^2x is (e^2x^4)/4+C

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integral of x^2e^2x

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

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

Solution steps

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

Simplify

x^{2} x : x^{3}

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

Apply the Power Rule

: \frac{x ^{4}}{4}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

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