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

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

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integral of tan(x)csc(x)

\int tan (x) csc (x) d x

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int tan (x) csc (x) d x

Simplify

tan (x) csc (x) : sec (x)

= \int sec (x) d x

Use the common integral:

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

= ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ + C

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