What is the integral of ye^{xy}+cos(x+y) ?

The integral of ye^{xy}+cos(x+y) is sin(y+x)+e^{yx}+C

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integral of ye^{xy}+cos(x+y)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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