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Popular >

integral of x^3ex^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

: \frac{x ^{6}}{6}

= 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

Popular Examples

integral of (nx)(1-n)/n

\int (n x) \frac{1 - n}{n} d x

(\partial)/(\partial x)(x^2z)

\frac{\partial}{\partial x} (x^{2} z)

derivative of 9sin^3(x)

\frac{d}{d x} (9 sin^{3} (x))

sum from n=1 to infinity of (n^3)/(3n^2)

n = 1 \sum \infty \frac{n ^{3}}{3 n ^{2}}

derivative of x(4-x)

\frac{d}{d x} (x (4 - x))

Frequently Asked Questions (FAQ)

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