1.

cosec x cot x dxcosec x+ Cvil

Answer»

cosec(x) = 1/sin(x), and

cot(x) = cos(x)/sin(x) .

So, cosec(x)cot(x) = cos(x)/sin^2(x).

∫cos(x)/sin^2(x) dx : substitute sin(x) = u, du/cos(x) = dx.

Substituting in, we have

∫u^(-2)du = -u^(-1) + C.

Since u = sin(x), we have that ∫ = -1/sin(x) + C,

or ∫ = -cosec(x) + C.


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