What is the integral of (3x^2y-2xy^4+6x-7y) ?

The integral of (3x^2y-2xy^4+6x-7y) is 3x^2-7yx-y^4x^2+yx^3+C

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integral of (3x^2y-2xy^4+6x-7y)

\int (3 x^{2} y - 2 x y^{4} + 6 x - 7 y) d x

3 x^{2} - 7 y x - y^{4} x^{2} + y x^{3} + C

Solution steps

\int 3 x^{2} y - 2 x y^{4} + 6 x - 7 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 6 x d x - \int 7 y d x - \int 2 y^{4} x d x + \int 3 y x^{2} d x

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

\int 7 y d x = 7 y x

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

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

= 3 x^{2} - 7 y x - y^{4} x^{2} + y x^{3}

Add a constant to the solution

= 3 x^{2} - 7 y x - y^{4} x^{2} + y x^{3} + C

What is the integral of (3x^2y-2xy^4+6x-7y) ?
The integral of (3x^2y-2xy^4+6x-7y) is 3x^2-7yx-y^4x^2+yx^3+C