What is the integral of ycos(xy)+y+1 ?

The integral of ycos(xy)+y+1 is x+yx+sin(yx)+C

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integral of ycos(xy)+y+1

\int y cos (x y) + y + 1 d x

x + y x + sin (y x) + C

Solution steps

\int y cos (x y) + y + 1 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 1 d x + \int y d x + \int cos (y x) y d x

\int 1 d x = x

\int y d x = y x

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

= x + y x + sin (y x)

Add a constant to the solution

= x + y x + sin (y x) + C

What is the integral of ycos(xy)+y+1 ?
The integral of ycos(xy)+y+1 is x+yx+sin(yx)+C