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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

ln ∣ x + cos (x) ∣ + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + cos (x)

= ln ∣ x + cos (x) ∣

Add a constant to the solution

= ln ∣ x + cos (x) ∣ + C

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