If \( I_{n}=\int \cot ^{n} x d x \) then \( \mathrm{P}^{12: 22} \) ...

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If \( I_{n}=\int \cot ^{n} x d x \) then
\( \mathrm{P}^{12: 22} \)
\( I_{0}+I_{1}+2\left(I_{2}+I_{3}+\ldots+I_{8}\right)+I_{9}+I_{10} \) equal to:
W
(where \( u=\cot x \) )
(1) \( u+\frac{u^{2}}{2}+\ldots+\frac{u^{9}}{9} \)
(2) \( -\left(u+\frac{u^{2}}{2}+\ldots+\frac{u^{9}}{9}\right) \)
(3) \( -\left(u+\frac{u^{2}}{2 !}+\ldots+\frac{u^{9}}{9 !}\right) \)
(4) \( \frac{u}{2}+\frac{2 u^{2}}{3}+\ldots+\frac{9 u^{9}}{10} \)
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