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cos(x) cot(x) = cos(x) * 1/(tan(x)) = cos(x) * 1 / (sinx(x) / cos(x))

= cos2(x) / sin(x) = (1-sin2(x)) / sin(x) = 1/sin(x) - sin(x)

so the antiderivative of cos(x)cot(x) = log[abs(tan(x/2))]+cos(x)

This can also be written as log[abs((sin(x)/(cos(x)+1))]+cos(x) if we want everything in terms of x and not (x/2). The two answers are, of course, the same.

where log(x) refers to the natural log, often written ln(x).

We might write ln[|sin(x)|/|cos(x)+1|] +cos(x)

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โˆ™ 2011-05-31 03:08:52
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Q: Integral of cos x cot x?
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