Evaluate: `intcos e cxlog(cos e cx-cotx)dx`

Explanation

`int {cosec} x cdot log ({cosec} x-cot x) d x`
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Let log ({cosec} x-cot x)=t`
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Rightarrow frac{(-{cosec} times cot x+{cosec}^{2} x)}{({cosec} {cosec} x-cot x)}=frac{d t}{d x}`
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Rightarrow(frac{{cosec} x-cot x}{{cosec} x-cot x}) times {cosec} x d x=d t`
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Rightarrow {cosec} x d x=d t`
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Now, int {cosec} {x} cdot log ({cosec} {x}-cot x) d x`
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=int_{t^{2}} t . d t`
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=frac{t^{2}}{2}+C`
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