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Popular >

integral of xn(x)

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

Popular Examples

integral of sec^{13}(x)

\int sec^{13} (x) d x

f (x) = sinh (2 x)

integral from 0 to ln(2) of e^{x+2y}

\int_{0}^{l n (2)} e^{x + 2 y} d x

(\partial)/(\partial x)(2x*e^{xy})

\frac{\partial}{\partial x} (2 x \cdot e^{x y})

(\partial)/(\partial x)(x^2z+3z^2x+6(x+z))

\frac{\partial}{\partial x} (x^{2} z + 3 z^{2} x + 6 (x + z))

Frequently Asked Questions (FAQ)

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