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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int 1 d v

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

\int ln (1 + y^{2}) d y

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\int 3 x ln (x) d x

\frac{d}{d x} (cos (4 x))

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