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Integral of 1 divided by sinx cosx?


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Answered 2009-11-20 21:14:43

Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)
= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]
= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]
= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)
= Integral of tan x dx + Integral of cot x dx
= ln |sec x| + ln |sin x| + C

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