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

The integral of (cot(ln(x)))/x is ln|sin(ln(x))|+C

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

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

ln ∣ sin (ln (x)) ∣ + C

Solution steps

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

Apply u-substitution

: \int cot (u) d u

= \int cot (u) d u

Rewrite using trig identities

= \int \frac{cos ( u )}{sin ( 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 ∣ sin (ln (x)) ∣

Add a constant to the solution

= ln ∣ sin (ln (x)) ∣ + C

\int_{0}^{1} 2 x^{2} x^{2} + 4 d x

\int e^{- 0.02 x} d x

\int \frac{1}{( 2 x - 1 )} d x

t^{2} \frac{d y}{d t} - t = 1 + y + y t

y^{^{''}} = ey

What is the integral of (cot(ln(x)))/x ?
The integral of (cot(ln(x)))/x is ln|sin(ln(x))|+C