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Popular Calculus >

integral of x^3e^2

Solution

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

Solution

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

Solution steps

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

Apply the Power Rule

= 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

Graph

Popular Examples

integral of (1+t)^2

derivative of y=(2x+4)/(1-x)

(dN)/(dt)+N=Nte^{t+4}

integral from 0 to 1 of x^2e^{x^3}

(dy)/(dx)=-0.5y+x

Frequently Asked Questions (FAQ)

What is the integral of x^3e^2 ?
The integral of x^3e^2 is (e^2x^4)/4+C