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Popular >

integral of y^2x

Solution

\int y^{2} x d y

Solution

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

Solution steps

\int y^{2} x d y

Take the constant out:

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

= x \cdot \int y^{2} d y

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

x y y^{^{'}} = 4 x^{2} + y^{2}

derivative of-3x^{2/3}derivative of

- 3 x^{\frac{2}{3}}

derivative of (sin(x-1)/(cos(x)+1))

\frac{d}{d x} (\frac{sin ( x ) - 1}{cos ( x ) + 1})

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

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

derivative of arctan((x^2/y))

\frac{d}{d x} (arctan (\frac{x ^{2}}{y}))

Frequently Asked Questions (FAQ)

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