What is the integral of xe^{xy}cos(2x)-3 ?

The integral of xe^{xy}cos(2x)-3 is -3y+e^{xy}cos(2x)+C

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integral of xe^{xy}cos(2x)-3

\int x e^{x y} cos (2 x) - 3 d y

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

Solution steps

\int x e^{x y} cos (2 x) - 3 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 3 d y + \int cos (2 x) x e^{x y} d y

\int 3 d y = 3 y

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

= - 3 y + e^{x y} cos (2 x)

Add a constant to the solution

= - 3 y + e^{x y} cos (2 x) + C

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What is the integral of xe^{xy}cos(2x)-3 ?
The integral of xe^{xy}cos(2x)-3 is -3y+e^{xy}cos(2x)+C