Evaluate the integral. \[ \int_{1}^{8}\left(\frac{6}{x}-e^{-x}\right) d x \]

Step 1 ：Separate the integral into two parts: \(\int_{1}^{8}\frac{6}{x} dx\) and \(\int_{1}^{8}-e^{-x} dx\).

Step 2 ：Calculate the integral of each part separately. The integral of \(\frac{6}{x}\) is \(6*ln|x|\) and the integral of \(-e^{-x}\) is \(e^{-x}\).

Step 3 ：Evaluate these at the limits of 1 and 8.

Step 4 ：The integral of \(\frac{6}{x}\) from 1 to 8 is \(6*ln|8| - 6*ln|1| = 12.476649250079014\).

Step 5 ：The integral of \(-e^{-x}\) from 1 to 8 is \(-e^{-8} + e^{-1} = 0.3675439785435398\).

Step 6 ：Add these two results together to get the final result: \(12.476649250079014 + 0.3675439785435398 = 12.844193228622553\).

Step 7 ：Final Answer: The value of the integral is \(\boxed{12.844193228622553}\).