The marginal cost of producing the $x$ th baseball bat is given by: \[ C^{\prime}(x)=25+\frac{5 x}{\left(x^{2}+1\right)^{2}} \] Find the total accumulated cost for producing the first 10 baseball bats. Round to the nearest cent.

Step 1 ：The marginal cost of producing the \(x\) th baseball bat is given by: \(C'(x) = 25 + \frac{5x}{(x^2 + 1)^2}\)

Step 2 ：To find the total accumulated cost for producing the first 10 baseball bats, we need to integrate the marginal cost function from 1 to 10.

Step 3 ：The integral of the marginal cost function will give us the total cost function.

Step 4 ：Evaluating the total cost function at 10 and subtracting the value at 1 will give us the accumulated cost for the first 10 bats.

Step 5 ：The total accumulated cost for producing the first 10 baseball bats is \(\boxed{226.23}\)