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

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

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

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

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

Solution steps

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

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{t}{2})

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

Simplify

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

Add a constant to the solution

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

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