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Question
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
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Solution
Let I = `int (e^x.log(sin e^x))/tan(e^x).dx`
= `int log (sin e^x).e^x.cot (e^x) dx`
Put log (sin ex) = t
∴ `(1)/sin (e^x).cos(e^x).e^x dx` = dt
∴ ex . cot (ex) dx = dt
∴ I = `int t dt = t^2/(2) + c`
= `(1)/(2)[log (sine^x)]^2 + c`.
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