What is the integral of (cot(x))/2 ?

The integral of (cot(x))/2 is 1/2 ln|sin(x)|+C

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integral of (cot(x))/2

integral

\frac{cot ( x )}{2}

\frac{1}{2} ln ∣ sin (x) ∣ + C

Solution steps

\int \frac{cot ( x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int cot (x) d x

Rewrite using trig identities

= \frac{1}{2} \cdot \int \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = sin (x)

= \frac{1}{2} ln ∣ sin (x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ sin (x) ∣ + C

(a - x^{2})^{\frac{1}{2}}

sin^{3} (x) cos^{3} (x)

(\frac{( x - 1 )}{( x + 1 )})^{\frac{1}{2}}

sin^{2} (x) cos^{3} (x)

\frac{sin ( x )}{( 1 - sin ( x ) )}

What is the integral of (cot(x))/2 ?
The integral of (cot(x))/2 is 1/2 ln|sin(x)|+C