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

Popular >

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

\int \frac{1}{- x ^{2} + 2 x + 15} d x

\frac{6}{s} + \frac{32}{s ^{2} + 16}

\frac{8}{( s ^{2} + 1 ) ^{2}}

x^{2} \frac{d y}{d x} - y^{2} = 0

x \to 0 lim (x (ln (x))^{2})

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