Determine the following. \[ \int\left(\frac{11}{x}+\frac{x}{11}\right) d x \] \[ \int\left(\frac{11}{x}+\frac{x}{11}\right) d x=\square \]

Step 1 ：Integrate each term separately: \( \int \frac{11}{x} dx \) and \( \int \frac{x}{11} dx \)

Step 2 ：The integral of \( \frac{11}{x} \) is \( 11 \ln|x| \)

Step 3 ：The integral of \( \frac{x}{11} \) is \( \frac{x^2}{22} \)

Step 4 ：Add the two results together to get the final answer

Step 5 ：\( \boxed{\frac{x^2}{22} + 11\ln|x| + C} \)