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

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

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integral of 2ysin(x)-xsin(y)

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

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