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Popular Calculus >

integral of x^2ex

Solution

\int x^{2} e x d x

Solution

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

Solution steps

\int x^{2} e x d x

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

Multiply fractions:

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

What is the integral of x^2ex ?
The integral of x^2ex is (ex^4)/4+C