What is the integral of (4ye^{xy}-3x^2) ?

The integral of (4ye^{xy}-3x^2) is -x^3+4e^{yx}+C

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integral of (4ye^{xy}-3x^2)

\int (4 y e^{x y} - 3 x^{2}) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int (x + 3) x - 1 d x

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What is the integral of (4ye^{xy}-3x^2) ?
The integral of (4ye^{xy}-3x^2) is -x^3+4e^{yx}+C