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

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

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

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

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

Solution steps

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

Apply u-substitution

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

x \to 0 lim (x^{2} c x c x)

\frac{d}{d x} (tanh (x - 1))

\frac{d}{d x} (x^{2} - x^{4})

x^{4} - 4 x^{2} + 2, x^{2} - 2, - 2, - 1

y^{^{'}} = e^{\frac{y}{x}} + \frac{y}{x}

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