What is the integral of (e^{2y}-ycos(xy)) ?

The integral of (e^{2y}-ycos(xy)) is e^{2y}x-sin(yx)+C

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integral of (e^{2y}-ycos(xy))

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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What is the integral of (e^{2y}-ycos(xy)) ?
The integral of (e^{2y}-ycos(xy)) is e^{2y}x-sin(yx)+C