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

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

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integral of x-y^3+y^2sin(x)

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

- y^{3} x + \frac{x ^{2}}{2} - y^{2} cos (x) + C

Solution steps

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

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

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

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

= - y^{3} x + \frac{x ^{2}}{2} - y^{2} cos (x)

Add a constant to the solution

= - y^{3} x + \frac{x ^{2}}{2} - y^{2} cos (x) + C

(1 + x)^{- \frac{2}{5}}

\int e^{- k x} cos (w x) d x

3 y^{^{''}} - 6 y^{^{'}} + 30 y = e^{x} tan (3 x)

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

\int \frac{5 x ^{3} + 2}{x ^{3} - 5 x ^{2} + 4 x} d x

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