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

The integral of 1/((1+sin(x)+cos(x))) is ln|tan(x/2)+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

ln tan (\frac{x}{2}) + 1 + C

Solution steps

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

Apply u-substitution

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln tan (\frac{x}{2}) + 1

Add a constant to the solution

= ln tan (\frac{x}{2}) + 1 + C

What is the integral of 1/((1+sin(x)+cos(x))) ?
The integral of 1/((1+sin(x)+cos(x))) is ln|tan(x/2)+1|+C