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

The integral of e^xcos(y)-x-2 is -2x-(x^2)/2+cos(y)e^x+C

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

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

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

Add a constant to the solution

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

(sech (2 x))^{s i n (3 x)}

\int csc (x) d x

1 + cos^{2} (x)

\frac{d x}{d y} 2 - \frac{d y}{d x} sec (x) = 0

f (x) = \frac{2}{5 x + 3}

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