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Popular Calculus >

integral of xy^3

Solution

\int x y^{3} d x

Solution

\frac{y ^{3} x ^{2}}{2} + C

Solution steps

\int x y^{3} d x

Take the constant out:

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

= y^{3} \cdot \int x d x

Apply the Power Rule

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

Multiply fractions:

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

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

Add a constant to the solution

= \frac{y ^{3} x ^{2}}{2} + C

Graph

Popular Examples

integral of x^3tan^3(x^4)

y^'+1/(x+8)y=x^{-2},y(1)=5

derivative of ((x+1^3)/(x^{3/2)})

tangent of f(x)=4x-x^2,\at x=1

Frequently Asked Questions (FAQ)

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