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

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Answer 1 · 2016-06-27T08:06:20

$- ln (1 + cos x)$

spotting the pattern is the easiest way

we know from the chain rule that $d/dx ln(f(x)) = 1/(f(x) )* f'(x)$

here we have $(-f'(x)) / f(x)$ because $(1 + cos x)' = - sin x$

so the answer is simply $- ln (1 + cos x)$

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