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Popular >

integral of x^3y

Solution

\int x^{3} y d y

Solution

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

Solution steps

\int x^{3} y d y

Take the constant out:

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

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

Apply the Power Rule

: \frac{y ^{2}}{2}

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

(dy)/(dx)=3yx^2-3x^2

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

(d^2)/(dx^2)(1/(x^9))

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{9}})

derivative of 6cos(5x)

\frac{d}{d x} (6 cos (5 x))

integral of sqrt(9/(9-x^2))

\int \frac{9}{9 - x ^{2}} d x

(\partial)/(\partial x)(ln(x/4+y/(12)))

\frac{\partial}{\partial x} (ln (\frac{x}{4} + \frac{y}{12}))

Frequently Asked Questions (FAQ)

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