What is the integral of 2/(1+cos(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(1+cos(x))

\int \frac{2}{1 + cos ( x )} d x

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

Solution steps

\int \frac{2}{1 + cos ( x )} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{1 + cos ( x )} d x

Apply u-substitution

: \int 1 d u

= 2 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 2 \cdot 1 \cdot u

Substitute back

u = tan (\frac{x}{2})

= 2 \cdot 1 \cdot tan (\frac{x}{2})

Simplify

= 2 tan (\frac{x}{2})

Add a constant to the solution

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

\int sec^{2} (θ) sec (θ) d θ

\int \frac{( 16 x ^{3} )}{x ^{4} + 5} d x

\int sin (\frac{2 θ}{3}) d θ

\int 3 x^{- \frac{6}{7}} d x

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