What is the integral of (sin(x))/(1-cos(x)) ?

The integral of (sin(x))/(1-cos(x)) is ln|1-cos(x)|+C

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integral of (sin(x))/(1-cos(x))

\int \frac{sin ( x )}{1 - cos ( x )} d x

ln ∣ 1 - cos (x) ∣ + C

Solution steps

\int \frac{sin ( x )}{1 - cos ( x )} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 - cos (x)

= ln ∣ 1 - cos (x) ∣

Add a constant to the solution

= ln ∣ 1 - cos (x) ∣ + C

\int 2 csc (x) d x

\frac{d}{d x} (b cos (x) + x^{2} sin (x))

y \to - 1 lim (y^{3} - 2 y^{2} + 3 y - 4)

\frac{1}{2} + \frac{1}{2} cos (2 t)

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

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