SOLUTION: Prove the formula ∫ cscxcotxdx = −cscx + C

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Question 1190607: Prove the formula ∫ cscxcotxdx = −cscx + C
Answer by Alan3354(69443) About Me  (Show Source):
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Prove the formula ∫ cscxcotxdx = −cscx + C
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∫ cscxcotxdx = ∫ (cos(x)/sin^2(x) dx
u = sin(x)
du = cos(x)
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---> ∫ du/u^2 = ∫ u^-2 du = -u^-1 + c
= -1/sin(x) + c
= -csc(x) + C