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

Explanation

To solve the problem, we need to find the value of \( x \) such that the middle term in the binomial expansion of \( \left( \frac{1}{x} + x \sin x \right)^{10} \) is equal to \( \frac{63}{8} \).

### Step-by-Step Solution:

1. **Identify the number of terms in the expansion**:
The binomial expansion of \( (a + b)^n \) has \( n + 1 \) terms. Here, \( n = 10 \), so there are \( 10 + 1 = 11 \) terms.

**Hint**: Remember that the number of terms in the expansion is \( n + 1 \).
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