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Popular >

integral of x^2Inx

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

: \frac{x ^{4}}{4}

= 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

Popular Examples

(\partial)/(\partial y)(6x^{y/z})

\frac{\partial}{\partial y} (6 x^{\frac{y}{z}})

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

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

integral of (x^4+x^2+4)/(x^2-4)

\int \frac{x ^{4} + x ^{2} + 4}{x ^{2} - 4} d x

integral of (4x^2)/(sqrt(x^3+16))

\int \frac{4 x ^{2}}{x ^{3} + 16} d x

derivative of y=x^{5/3}-x^{2/3}derivative of

y = x^{\frac{5}{3}} - x^{\frac{2}{3}}

Frequently Asked Questions (FAQ)

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