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speeding electron
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Int(cosec x)dx Let: u=cos x then: x=arcos u and: dx=-du/sqrt(1-u^2)
Int(cosec x)dx = -Int{1/sqrt(1-u^2)}^2}du = -Int {du/(1-u^2)}
= -(1/2)ln(1-u^2) + C
= -(1/2)ln(sin^[2]x) +C
= ln(cosec x) +C
Yet differentiating back gives -cot x.
Why does this substitution not work?
Int(cosec x)dx = -Int{1/sqrt(1-u^2)}^2}du = -Int {du/(1-u^2)}
= -(1/2)ln(1-u^2) + C
= -(1/2)ln(sin^[2]x) +C
= ln(cosec x) +C
Yet differentiating back gives -cot x.
Why does this substitution not work?
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