Mathematics

Problem

I_n = \int \cot^n x\,dx

, then

I_0 + I_1 + 2\left(I_2 + I_3 + \dots + I_8\right) + I_9 + I_{10}

equals to (where

u = \cot x

) a.

u + \frac{u^2}{2} + \dots + \frac{u^9}{9}

- \left( u + \frac{u^2}{2} + \dots + \frac{u^9}{9} \right)

- \left( u + \frac{u^2}{2!} + \dots + \frac{u^9}{9!} \right)

\frac{u}{2} + \frac{2u^2}{3} + \dots + \frac{9u^9}{10}