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Popular Calculus >

integral of 2xy^3

Solution

\int 2 x y^{3} d x

Solution

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

Solution steps

\int 2 x y^{3} d x

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

= y^{3} x^{2}

Add a constant to the solution

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

Graph

Popular Examples

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\int x^{2} cos (3 x) d x

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\int \frac{r ^{3}}{16 + r ^{2}} d r

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\int_{0}^{6} ∣ x - 4 ∣ d x

derivative of ln((x+6^{11}))

\frac{d}{d x} (ln ((x + 6)^{11}))

integral from 0 to 0.1 of xarctan(3x)

\int_{0}^{0.1} x arctan (3 x) d x

Frequently Asked Questions (FAQ)

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