What is the integral of (sin(s))/(1+cos(s)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(s))/(1+cos(s))

\int \frac{sin ( s )}{1 + cos ( s )} d s

- ln ∣ 1 + cos (s) ∣ + C

Solution steps

\int \frac{sin ( s )}{1 + cos ( s )} d s

Apply u-substitution

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

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

Take the constant out:

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

= - \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 (s)

= - ln ∣ 1 + cos (s) ∣

Add a constant to the solution

= - ln ∣ 1 + cos (s) ∣ + C

2 + 0.45 sin (\frac{2 π x}{4.5})

\frac{d}{d x} (\frac{1}{∣ x ∣})

\int x sin (\frac{x}{3}) d x

\int - ln (x + 1) d x

\frac{d}{d x} (\frac{b}{cos ( θ )})

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