What is the integral of-e^y-ycos(xy) ?

The integral of-e^y-ycos(xy) is -e^yx-sin(yx)+C

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integral of-e^y-ycos(xy)

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

- e^{y} x - sin (y x) + C

Solution steps

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

\int e^{y} d x = e^{y} x

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

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

Add a constant to the solution

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

What is the integral of-e^y-ycos(xy) ?
The integral of-e^y-ycos(xy) is -e^yx-sin(yx)+C