What is the integral of (3+3cot(x)) ?

The integral of (3+3cot(x)) is 3x+3ln|sin(x)|+C

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integral of (3+3cot(x))

\int (3 + 3 cot (x)) d x

3 x + 3 ln ∣ sin (x) ∣ + C

Solution steps

\int 3 + 3 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 3 d x + \int 3 cot (x) d x

\int 3 d x = 3 x

\int 3 cot (x) d x = 3 ln ∣ sin (x) ∣

= 3 x + 3 ln ∣ sin (x) ∣

Add a constant to the solution

= 3 x + 3 ln ∣ sin (x) ∣ + C

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What is the integral of (3+3cot(x)) ?
The integral of (3+3cot(x)) is 3x+3ln|sin(x)|+C