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 x} (e^{- 7 x} cos (10 x))

f (x) = 10 - 4 e^{x}, (0, 6)

\frac{d}{d x} (sin (4))

\frac{d}{d x} (ln (x - 1) + 1)

x \to 2 lim (x ln (\frac{x}{x - 2}))

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