What is the antiderivative of $cot(x)$ ?

Question

32073 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-24T03:01:37

$intcotxdx=ln|sinx|+C$

Recall that $cotx=cosx/sinx.$ Thus,

$intcotxdx=intcosx/sinxdx$

We can solve this with a simple substitution.

$u=sinx$

$du=cosxdx$

This appears in our numerator, so the substitution is indeed valid.

So, we have

$int(du)/u=ln|u|+C=ln|sinx|+C$

$intcotxdx=ln|sinx|+C$

What is the antiderivative of cot(x)cot(x)?