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

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

Popular >

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

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

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

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

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

= \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

\int (\frac{8 x ^{2}}{( x ^{3} + 2 ) ^{3}}) d x

\int 7 x^{- \frac{1}{2}} d x

\int 8 \cdot cos (x) + \frac{1}{x} + e^{3 x} d x

\int 5 t^{2} d t

\int (4 x^{3} + 8 x + 5) d x

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