What is the integral of (2x^2y-3xy^2+2) ?

The integral of (2x^2y-3xy^2+2) is 2y+x^2y^2-xy^3+C

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integral of (2x^2y-3xy^2+2)

\int (2 x^{2} y - 3 x y^{2} + 2) d y

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

Solution steps

\int 2 x^{2} y - 3 x y^{2} + 2 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 d y + \int 2 x^{2} y d y - \int 3 x y^{2} d y

\int 2 d y = 2 y

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

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

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

Add a constant to the solution

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

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\int x^{2021} d x

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

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