What is the integral of (8x^3y-y^3) ?

The integral of (8x^3y-y^3) is -y^3x+2yx^4+C

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integral of (8x^3y-y^3)

\int (8 x^{3} y - y^{3}) d x

- y^{3} x + 2 y x^{4} + C

Solution steps

\int 8 x^{3} y - y^{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 y^{3} d x + \int 8 y x^{3} d x

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

\int 8 y x^{3} d x = 2 y x^{4}

= - y^{3} x + 2 y x^{4}

Add a constant to the solution

= - y^{3} x + 2 y x^{4} + C

What is the integral of (8x^3y-y^3) ?
The integral of (8x^3y-y^3) is -y^3x+2yx^4+C