What is the integral of-xsin(y)+2y ?

The integral of-xsin(y)+2y is y^2+xcos(y)+C

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integral of-xsin(y)+2y

\int - x sin (y) + 2 y d y

y^{2} + x cos (y) + C

Solution steps

\int - x sin (y) + 2 y d y

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 y d y - \int sin (y) x d y

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

\int sin (y) x d y = - x cos (y)

= y^{2} - (- x cos (y))

Simplify

= y^{2} + x cos (y)

Add a constant to the solution

= y^{2} + x cos (y) + C

\int x (x + 9)^{10} d x

\int \frac{sec ( x )}{tan ( x )} d x

y^{23} d y = x d x

x \to 0 lim (\frac{3}{x ( x - 1 )})

\int \frac{x ^{3}}{x ^{2} + 81} d x

What is the integral of-xsin(y)+2y ?
The integral of-xsin(y)+2y is y^2+xcos(y)+C