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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int (2 x - 7)^{73} d x

\int sin (2 x) 2 d x

\int 16 - 9 u^{2} d u

\int tan^{3} (2 x) sec^{6} (2 x) 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