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Popular >

integral of xnx

Solution

\int x n x d x

Solution

\frac{n x ^{3}}{3} + C

Solution steps

\int x n x d x

Take the constant out:

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

= n \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= n \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{n x ^{3}}{3}

Add a constant to the solution

= \frac{n x ^{3}}{3} + C

Graph

Popular Examples

derivative of sin(θ)+cos(θ)θ derivative of

sin (θ) + cos (θ) θ

integral of (x^2)/(1-x)

\int \frac{x ^{2}}{1 - x} d x

integral of (4u)/(16u^2+7)

\int \frac{4 u}{16 u ^{2} + 7} d u

derivative of e^{9xsin(2x})

\frac{d}{d x} (e^{9 x s i n (2 x)})

sum from n=1 to infinity of (cos(n))/(n^5)

n = 1 \sum \infty \frac{cos ( n )}{n ^{5}}

Frequently Asked Questions (FAQ)

What is the integral of xnx ?
The integral of xnx is (nx^3)/3+C