Evaluate the integral.
$\int_{1}^{8} (\frac{6}{x} - e^{- x}) d x$

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Final Answer: The value of the integral is $12.844193228622553$ .

Steps

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

Step 2 ：Calculate the integral of each part separately. The integral of $\frac{6}{x}$ is $6 * l n | x |$ 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 $6 * l n | 8 | - 6 * l n | 1 | = 12.476649250079014$ .

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 $12.844193228622553$ .

Evaluate the integral.∫18(6x−e−x)dx

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Popular Problems

Evaluate the integral.
$\int_{1}^{8} (\frac{6}{x} - e^{- x}) d x$