Question
Integrate the function: cot x log sin x
Putting log sin x = t
$ \Rightarrow \frac{1}{{\sin x}}\frac{d}{{dx}}\left( {\sin x} \right) = \frac{{dt}}{{dx}}$
$ \Rightarrow \frac{1}{{\sin x}}\cos x = \frac{{dt}}{{dx}}$
$ \Rightarrow \cot xdx = dt$
$\therefore$ From eq. (i), $I = \int {tdt} $
$ = \frac{{{t^2}}}{2} + c$
$= \frac{1}{2}{\left( {\log \sin x} \right)^2} + c$
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| $X_i$ | $0$ | $1$ | $2$ |
| $P_i$ | $3c^3$ | $4c - 10c^2$ | $5c - 1$ |