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Popular Calculus >

integral of 2x^3y

Solution

\int 2 x^{3} y d y

Solution

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

Solution steps

\int 2 x^{3} y d y

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

= x^{3} y^{2}

Add a constant to the solution

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

Graph

Popular Examples

integral of 2t^2e^{-t}

\int 2 t^{2} e^{- t} d t

integral of (x^2)/(x^2+x+72)

\int \frac{x ^{2}}{x ^{2} + x + 72} d x

integral of ln^2(2/x)

\int ln^{2} (\frac{2}{x}) d x

integral of (x^3+4x^2+7x+6)/(x^2+3x+4)

\int \frac{x ^{3} + 4 x ^{2} + 7 x + 6}{x ^{2} + 3 x + 4} d x

integral of (2x^5+5x^4+2x^3-3/(x^2)+4)

\int (2 x^{5} + 5 x^{4} + 2 x^{3} - \frac{3}{x ^{2}} + 4) d x

Frequently Asked Questions (FAQ)

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