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Popular >

integral of x^3y^2

Solution

\int x^{3} y^{2} d y

Solution

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

Solution steps

\int x^{3} y^{2} 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^{2} d y

Apply the Power Rule

: \frac{y ^{3}}{3}

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/(xsqrt(4+x^2))

\int \frac{1}{x 4 + x ^{2}} d x

y^{^{'}} = k y

y^{''}-y^'-2y=4x^2,y(0)=-1,y^'(0)=1

y^{^{''}} - y^{^{'}} - 2 y = 4 x^{2}, y (0) = - 1, y^{^{'}} (0) = 1

limit as x approaches 16 of sqrt(4x)

x \to 16 lim (4 x)

integral from 0 to 5 of pi((20-4x)/5)^2

\int_{0}^{5} π (\frac{20 - 4 x}{5})^{2} d x

Frequently Asked Questions (FAQ)

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