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

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

Popular >

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

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

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

Solution steps

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

Simplify

= 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{sec ( y ) tan ( y )}{5 + 4 sec ^{2} ( y )} d y

\int \frac{x ^{6} + 8}{x ^{5}} d x

\int sec^{2} (\frac{x}{5}) d x

\int \frac{1}{y ( ln ( y ^{2} ) + c )} d y

\int (3 x + cos (3 x)) d x

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