-cotan(x)
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d/dx cosec(x) = - cosec(x) * cot(x) so the second derivative or d(d/dx)/dx cosec(x) = [- cosec(x) * d/dx cot(x)] + [ - d/dx cosec(x) * cot(x)] = [- cosec(x) * -cosec^2(x)] + [ - (- cosec(x) * cot(x)) * cot(x)] = cosec(x) * cosec^2(x) + cosec(x)*cot^2(x) = cosec(x) * [cosec^2(x) + cot^2(x)].
.5(x-sin(x)cos(x))+c
the integral of the square-root of (x-1)2 = x2/2 - x + C
(x+sinxcosx)/2, can do it by parts or by knowing your double angle formulas
Cot x is 1/tan x or cos x / sin x or +- sqrt cosec^2 x -1