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 (9 - 4 x)^{10} d x

\int (- 4 sec^{2} (x)) d x

\int \frac{1}{( 1 + x ) ^{\frac{3}{2}}} d x

\int (x^{2} - 2 x + 1) cos (x) d x

\frac{x}{x ^{2} + 1}

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