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

The integral of csc(x)+cot(x) is ln|tan(x/2)|+ln|sin(x)|+C

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integral of csc(x)+cot(x)

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

ln tan (\frac{x}{2}) + ln ∣ sin (x) ∣ + C

Solution steps

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

\int csc (x) d x = ln tan (\frac{x}{2})

\int cot (x) d x = ln ∣ sin (x) ∣

= ln tan (\frac{x}{2}) + ln ∣ sin (x) ∣

Add a constant to the solution

= ln tan (\frac{x}{2}) + ln ∣ sin (x) ∣ + C

What is the integral of csc(x)+cot(x) ?
The integral of csc(x)+cot(x) is ln|tan(x/2)|+ln|sin(x)|+C