What are the antiderivatives of $sec (x)$ $sec(x)$ , $csc (x)$ $csc(x)$ and $cot (x)$ $cot(x)$ ?

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Answer 1 · 2014-10-16T16:54:49

Since

$(ln|secx+tanx|)'={secxtanx+sec^2x}/{sec x+tanx}=secx$ ,

we have

$int secx dx=ln|secx+tanx|+C$

Since

$(-ln|cscx+cotx|)'=-{-cscxcotx-csc^2x}/{cscx+cotx}=cscx$ ,

we have

$int cscx dx=-ln|cscx+cotx|+C$

$int cotx dx=int{cosx}/{sinx}dx=ln|sinx|+C$

I hope that this was helpful.

What are the antiderivatives of sec(x)sec(x)sec(x), csc(x)csc(x)csc(x) and cot(x)cot(x)cot(x)?