What is the integral of (sec(x)csc(x))/(ln(tan(x))) ?

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

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integral of (sec(x)csc(x))/(ln(tan(x)))

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

ln ∣ ln (tan (x)) ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ln ( u )} d u

= \int \frac{1}{u ln ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ ln (tan (x)) ∣

Add a constant to the solution

= ln ∣ ln (tan (x)) ∣ + C

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