What is the integral of (cos(x)cos(y)-cot(x)) ?

The integral of (cos(x)cos(y)-cot(x)) is -ln|sin(x)|+cos(y)sin(x)+C

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integral of (cos(x)cos(y)-cot(x))

\int (cos (x) cos (y) - cot (x)) d x

- ln ∣ sin (x) ∣ + cos (y) sin (x) + C

Solution steps

\int cos (x) cos (y) - cot (x) 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 cot (x) d x + \int cos (y) cos (x) d x

\int cot (x) d x = ln ∣ sin (x) ∣

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

= - ln ∣ sin (x) ∣ + cos (y) sin (x)

Add a constant to the solution

= - ln ∣ sin (x) ∣ + cos (y) sin (x) + C

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What is the integral of (cos(x)cos(y)-cot(x)) ?
The integral of (cos(x)cos(y)-cot(x)) is -ln|sin(x)|+cos(y)sin(x)+C