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Popular Calculus >

integral of (2x^2y)

Solution

\int (2 x^{2} y) d y

Solution

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

Solution steps

\int 2 x^{2} y d y

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

= x^{2} y^{2}

Add a constant to the solution

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

Graph

Popular Examples

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

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

integral of (-2)/(7x^4)

\int \frac{- 2}{7 x ^{4}} d x

integral of 2xsin(6x)

\int 2 x sin (6 x) d x

integral of (x^4)/((1-x^2)^3)

\int \frac{x ^{4}}{( 1 - x ^{2} ) ^{3}} d x

integral of (x^3ln(x))/2

\int \frac{x ^{3} ln ( x )}{2} d x

Frequently Asked Questions (FAQ)

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