What is the integral of csc(θ)tan(θ) ?

The integral of csc(θ)tan(θ) is ln|tan(θ)+sec(θ)|+C

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integral of csc(θ)tan(θ)

\int csc (θ) tan (θ) d θ

ln ∣ tan (θ) + sec (θ) ∣ + C

Solution steps

\int csc (θ) tan (θ) d θ

Simplify

csc (θ) tan (θ) : sec (θ)

= \int sec (θ) d θ

Use the common integral:

\int sec (θ) d θ = ln ∣ tan (θ) + sec (θ) ∣

= ln ∣ tan (θ) + sec (θ) ∣

Add a constant to the solution

= ln ∣ tan (θ) + sec (θ) ∣ + C

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What is the integral of csc(θ)tan(θ) ?
The integral of csc(θ)tan(θ) is ln|tan(θ)+sec(θ)|+C