What is the integral of (e^xcos(y)-x-2) ?

The integral of (e^xcos(y)-x-2) is -2y-xy+e^xsin(y)+C

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integral of (e^xcos(y)-x-2)

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

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

Solution steps

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

\int 2 d y = 2 y

\int x d y = x y

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

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

Add a constant to the solution

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

\int f^{2} (x) d x

\frac{d}{d x} ((2 x - 3)^{3})

\frac{\partial}{\partial x} (4 x + y)

\int 4 e^{2 x - 1} d x

\int_{- 1}^{1} \frac{1}{t + 1} d t

What is the integral of (e^xcos(y)-x-2) ?
The integral of (e^xcos(y)-x-2) is -2y-xy+e^xsin(y)+C