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Popular Calculus >

integral of xin(x)

Solution

\int x in (x) d x

Solution

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

Solution steps

\int x in x d x

Take the constant out:

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

= in \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

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

Multiply fractions:

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral from 0 to 1/2 of xsqrt(1-4x^2)

\int_{0}^{\frac{1}{2}} x 1 - 4 x^{2} d x

(\partial)/(\partial x)(e^yx)

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

y^'= x/(200)-y/(100)

y^{^{'}} = \frac{x}{200} - \frac{y}{100}

ma c l a u r in 2^{x}

integral of ysin(x)

\int y sin (x) d x

Frequently Asked Questions (FAQ)

What is the integral of xin(x) ?
The integral of xin(x) is (inx^3)/3+C