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

The integral of (csc(ln(x))cot(ln(x)))/x is -csc(ln(x))+C

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integral of (csc(ln(x))cot(ln(x)))/x

\int \frac{csc ( ln ( x ) ) cot ( ln ( x ) )}{x} d x

- csc (ln (x)) + C

Solution steps

\int \frac{csc ( ln ( x ) ) cot ( ln ( x ) )}{x} d x

Apply u-substitution

: \int csc (u) cot (u) d u

= \int csc (u) cot (u) d u

Apply u-substitution

: \int - 1 d v

= \int - 1 d v

Integral of a constant:

\int a d x = a x

= (- 1) v

Substitute back

= (- 1) csc (ln (x))

Simplify

= - csc (ln (x))

Add a constant to the solution

= - csc (ln (x)) + C

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What is the integral of (csc(ln(x))cot(ln(x)))/x ?
The integral of (csc(ln(x))cot(ln(x)))/x is -csc(ln(x))+C