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Popular Calculus >

integral of x^2ex^3

Solution

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

Solution

\frac{e x ^{6}}{6} + C

Solution steps

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

Simplify

x^{2} x^{3} : x^{5}

= e \cdot \int x^{5} d x

Apply the Power Rule

= e \frac{x ^{6}}{6}

Multiply fractions:

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

= \frac{e x ^{6}}{6}

Add a constant to the solution

= \frac{e x ^{6}}{6} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of x^2ex^3 ?
The integral of x^2ex^3 is (ex^6)/6+C