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If I(n)=int cot^(n) x dx, then I(0)+I(1)...

If `I_(n)=int cot^(n) x dx`, then `I_(0)+I_(1)+2(I_(2)+I_(3)+...+I_(8))+I_(9)+I_(10)` equals to (where `u=cot x`)

A

`u+(u^(2))/(2)+...+(u^(9))/(9)`

B

`-(u+(u^(2))/(2)+...+(u^(9))/(9))`

C

`-(u+(u^(2))/(2!)+...+(u^(9))/(9!))`

D

`u/2 + (2u^(2))/(3)+...+(9u^(9))/(10)`

Text Solution

Verified by Experts

The correct Answer is:
B
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