What is the integral of 2x+ycos(xy) ?

The integral of 2x+ycos(xy) is x^2+sin(yx)+C

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integral of 2x+ycos(xy)

\int 2 x + y cos (x y) d x

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

Solution steps

\int 2 x + 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 2 x d x + \int cos (y x) y d x

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

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

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

Add a constant to the solution

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

What is the integral of 2x+ycos(xy) ?
The integral of 2x+ycos(xy) is x^2+sin(yx)+C