Evaluate the following indefinite integral. \[ \int\left(11 x^{10}-\frac{10}{x^{10}}\right) d x \] \[ \int\left(11 x^{10}-\frac{10}{x^{10}}\right) d x=\square \]

Step 1 ：Given the integral \(\int\left(11 x^{10}-\frac{10}{x^{10}}\right) d x\)

Step 2 ：We can split this integral into two parts: \(\int 11 x^{10} dx\) and \(\int -\frac{10}{x^{10}} dx\)

Step 3 ：The integral of \(11 x^{10}\) with respect to \(x\) is \(\frac{1}{10+1} \cdot 11 \cdot x^{10+1} = x^{11}\)

Step 4 ：The integral of \(-\frac{10}{x^{10}}\) with respect to \(x\) is \(-\frac{1}{10-1} \cdot -10 \cdot x^{1-10} = \frac{10}{9x^9}\)

Step 5 ：Adding these two integrals together, we get \(x^{11} + \frac{10}{9x^9}\)

Step 6 ：So, the solution to the integral \(\int\left(11 x^{10}-\frac{10}{x^{10}}\right) d x\) is \(\boxed{x^{11} + \frac{10}{9x^9}}\)