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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

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