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

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

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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

= 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

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