What is the integral of (tan(θ)+cot(θ)) ?

The integral of (tan(θ)+cot(θ)) is -ln|cos(θ)|+ln|sin(θ)|+C

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integral of (tan(θ)+cot(θ))

\int (tan (θ) + cot (θ)) d θ

- ln ∣ cos (θ) ∣ + ln ∣ sin (θ) ∣ + C

Solution steps

\int tan (θ) + cot (θ) d θ

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 (θ) d θ + \int cot (θ) d θ

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

\int cot (θ) d θ = ln ∣ sin (θ) ∣

= - ln ∣ cos (θ) ∣ + ln ∣ sin (θ) ∣

Add a constant to the solution

= - ln ∣ cos (θ) ∣ + ln ∣ sin (θ) ∣ + C

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