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Popular Calculus >

integral of x^2In(x)

Solution

\int x^{2} I n (x) d x

Solution

\frac{I n x ^{4}}{4} + C

Solution steps

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

Simplify

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

= I n \cdot \int x^{3} d x

Apply the Power Rule

= I n \frac{x ^{4}}{4}

Multiply fractions:

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

= \frac{I n x ^{4}}{4}

Add a constant to the solution

= \frac{I n x ^{4}}{4} + C

Graph

Popular Examples

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limit as x approaches 4 of sqrt(4)

Frequently Asked Questions (FAQ)

What is the integral of x^2In(x) ?
The integral of x^2In(x) is (Inx^4)/4+C