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

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

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integral of (2xy^2-3)

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

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

Solution steps

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

Apply the Sum Rule:

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

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

\int 3 d x = 3 x

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

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

Add a constant to the solution

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

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