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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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