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

The integral of (y^2cos(x)-3x^2y-2x) is -x^2+y^2sin(x)-yx^3+C

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integral of (y^2cos(x)-3x^2y-2x)

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

- x^{2} + y^{2} sin (x) - y x^{3} + C

Solution steps

\int y^{2} cos (x) - 3 x^{2} y - 2 x 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 2 x d x + \int cos (x) y^{2} d x - \int 3 y x^{2} d x

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

\int cos (x) y^{2} d x = y^{2} sin (x)

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

= - x^{2} + y^{2} sin (x) - y x^{3}

Add a constant to the solution

= - x^{2} + y^{2} sin (x) - y x^{3} + C

\frac{\partial}{\partial z} (ln (x y))

x^{3} - 4 x^{2}, 2 x^{2} - 8 x

\frac{1}{( s ^{2} + 1 ) ( s ^{2} + 3 s )}

\int \frac{24 x ^{3} - 48 x ^{2} + 7}{x ^{2} - 2 x} d x

(2 x ln (x) + x^{2} - 1)^{^{'}}

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