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

= \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

\frac{d}{d x} (5 x 64 - x^{2})

\frac{x}{1 - x ^{2}}

f (x) = 8 x

\frac{d}{d x} (lo g_{3} (x e^{x}))

y = (x^{3} - 4 x)^{8}, (2, 0)

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