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Popular >

integral of 2xyz^3

Solution

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

Solution

x z^{3} y^{2} + C

Solution steps

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

Take the constant out:

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

= 2 x z^{3} \cdot \int y d y

Apply the Power Rule

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

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

Simplify

2 x z^{3} \frac{y ^{2}}{2} : x z^{3} y^{2}

= x z^{3} y^{2}

Add a constant to the solution

= x z^{3} y^{2} + C

Popular Examples

(dy)/(dx)=15-3y

\frac{d y}{d x} = 15 - 3 y

limit as x approaches 0 of (sin^6(x))/x

x \to 0 lim (\frac{sin ^{6} ( x )}{x})

(\partial)/(\partial y)(x^2sin^2(y))

\frac{\partial}{\partial y} (x^{2} sin^{2} (y))

derivative of 1^{1/3}

\frac{d}{d x} (1^{\frac{1}{3}})

x^2y^{''}+3xy^'+y= 1/x

x^{2} y^{^{''}} + 3 x y^{^{'}} + y = \frac{1}{x}

Frequently Asked Questions (FAQ)

What is the integral of 2xyz^3 ?
The integral of 2xyz^3 is xz^3y^2+C