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Popular Calculus >

integral of xin^2x

Solution

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

Solution

\frac{i n ^{2} x ^{3}}{3} + C

Solution steps

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

Take the constant out:

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

= i n^{2} \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

= i n^{2} \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{i n ^{2} x ^{3}}{3}

Add a constant to the solution

= \frac{i n ^{2} x ^{3}}{3} + C

Graph

Popular Examples

integral of sec(x)

integral of u/(1-u^2)

derivative of 2ln(4x)

derivative of (sqrt(x)/3)

(\partial)/(\partial x)(1/(r^2))

Frequently Asked Questions (FAQ)

What is the integral of xin^2x ?
The integral of xin^2x is (in^2x^3)/3+C