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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- ln ∣ 1 - sin (x) ∣ + C

Solution steps

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

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 - sin (x)

= - ln ∣ 1 - sin (x) ∣

Add a constant to the solution

= - ln ∣ 1 - sin (x) ∣ + C

n = 0 \sum \infty \frac{1}{( 4 n ^{2} - 1 )}

\int_{8}^{\infty} x e^{- 2 x} d x

\frac{d}{d x} (sin^{3} (x) + sin (3 x))

\frac{d}{d y} (tan (x) + y)

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

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