What is the integral of 6x^2y-3xsqrt(y) ?

The integral of 6x^2y-3xsqrt(y) is -(3sqrt(y)x^2)/2+2yx^3+C

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integral of 6x^2y-3xsqrt(y)

\int 6 x^{2} y - 3 x y d x

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

Solution steps

\int 6 x^{2} y - 3 x 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 3 y x d x + \int 6 y x^{2} d x

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

\int 6 y x^{2} d x = 2 y x^{3}

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

Add a constant to the solution

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

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What is the integral of 6x^2y-3xsqrt(y) ?
The integral of 6x^2y-3xsqrt(y) is -(3sqrt(y)x^2)/2+2yx^3+C