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Popular Calculus >

integral of xIn(x)

Solution

\int x I n (x) d x

Solution

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

Solution steps

\int x I n x d x

Take the constant out:

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

= I n \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

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

Multiply fractions:

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

What is the integral of xIn(x) ?
The integral of xIn(x) is (Inx^3)/3+C