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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

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