What is the integral of 4x^3-12xy^2 ?

The integral of 4x^3-12xy^2 is 4x^3y-4xy^3+C

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integral of 4x^3-12xy^2

\int 4 x^{3} - 12 x y^{2} d y

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

Solution steps

\int 4 x^{3} - 12 x y^{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 4 x^{3} d y - \int 12 x y^{2} d y

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

\int 12 x y^{2} d y = 4 x y^{3}

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

Add a constant to the solution

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

\int \frac{x ^{2} - 4 x + 4}{x ^{2} - 4 x + 29} d x

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\int \frac{t ^{2}}{3 6 + t ^{3}} d t

\int 2 x - 5^{x} + \frac{3}{x} d x

What is the integral of 4x^3-12xy^2 ?
The integral of 4x^3-12xy^2 is 4x^3y-4xy^3+C