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Popular >

integral of 4xy^3

Solution

\int 4 x y^{3} d x

Solution

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

Solution steps

\int 4 x y^{3} d x

Take the constant out:

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

= 4 y^{3} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= 4 y^{3} \frac{x ^{2}}{2}

Simplify

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

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

Add a constant to the solution

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

Popular Examples

derivative of f(x)=sqrt(2x+3)derivative of

f (x) = 2 x + 3

integral of 5x^2-6x

\int 5 x^{2} - 6 x d x

(dx)/(dt)= 6/(t+4)

\frac{d x}{d t} = \frac{6}{t + 4}

integral from-1 to 2 of (x+2)-x^2

\int_{- 1}^{2} (x + 2) - x^{2} d x

derivative of arccsc(-7x^2)

\frac{d}{d x} (arccsc (- 7 x^{2}))

Frequently Asked Questions (FAQ)

What is the integral of 4xy^3 ?
The integral of 4xy^3 is 2y^3x^2+C