What is the integral of (tan(4s)-cot(s/4)) ?

The integral of (tan(4s)-cot(s/4)) is -1/4 ln|cos(4s)|-4ln|sin(s/4)|+C

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integral of (tan(4s)-cot(s/4))

\int (tan (4 s) - cot (\frac{s}{4})) d s

- \frac{1}{4} ln ∣ cos (4 s) ∣ - 4 ln sin (\frac{s}{4}) + C

Solution steps

\int tan (4 s) - cot (\frac{s}{4}) d s

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int tan (4 s) d s - \int cot (\frac{s}{4}) d s

\int tan (4 s) d s = - \frac{1}{4} ln ∣ cos (4 s) ∣

\int cot (\frac{s}{4}) d s = 4 ln sin (\frac{s}{4})

= - \frac{1}{4} ln ∣ cos (4 s) ∣ - 4 ln sin (\frac{s}{4})

Add a constant to the solution

= - \frac{1}{4} ln ∣ cos (4 s) ∣ - 4 ln sin (\frac{s}{4}) + C

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What is the integral of (tan(4s)-cot(s/4)) ?
The integral of (tan(4s)-cot(s/4)) is -1/4 ln|cos(4s)|-4ln|sin(s/4)|+C