How do you find the antiderivative of $1/(1+cosx)$ ?

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Answer 1 · 2016-07-11T20:12:07

$=tan (x/2) + C$

$int dx qquad 1/(1 + cos x)$

double angle formula $cos 2A = 2 cos^2 A -1$

so $cos x = 2 cos^2 (x/2) -1$

$impliesint dx qquad 1/2 sec^2 (x/2)$

we know that $d/(du) tan u = sec^2 u$ so $d/(du) tan (u/2) = sec^2 (u/2) * 1/2$

so we can play with that idea and FTC to get

$tan (x/2) + C$

How do you find the antiderivative of 1/(1+cosx)1/(1+cosx)?