Evaluate: `1/(1+cosx)\ dx`

Explanation

Solution:

`\int \frac{1}{1+\cos x} {~d} x =\int \frac{1}{2 \cos ^{2}(\frac{x}{2})} {d} x`

=`\frac{1}{2} \int \sec ^{2}(\frac{x}{2}) {d} x `

=`\frac{1}{2}[\frac{\tan (\frac{x}{2})}{\frac{1}{2}}]+{c}`

=`\tan (\frac{x}{2})+{c}`