If the middle term in the binomial expansion of `(1/x+xsinx^(10))` is equal to `(63)/8,` find the value of `xdot`

Answer

`x = npi + (-1)^(n)'(pi)/(6), n in Z`

Explanation

Here middle term is `T_(6)`.
`:. T_(6) = .^(10)C_(5) (1)/(x^(5)).x^(5) sin^(5)x = (63)/(8)`
or `sin^(5)x = (1)/(2^(5))`
or `sinx = 1/2`
`rArr x = npi + (-1)^(n) '(pi)/(6), n in Z`