Evaluate the improper integral int_{0}^{1} frac{ln x}{x} mathrm{~d} x

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Accepted Answer

Step:1 ：This is an improper integral because the function is not defined at x=0. We can solve this by taking the limit as the lower bound of the integral approaches 0 from the right.Step:2 ：We can use the formula for the integral of ln(x)/x, which is 0.5*(ln(x))^2.Step:3 ：The integral evaluates to negative infinity. This is because the function ln(x)/x approaches negative infinity as x approaches 0 from the right.Step:4 ：Final Answer: The value of the improper integral (int_{0}^{1} frac{ln x}{x} mathrm{~d} x) is (boxed{-infty}).

Answer

Step: 1 ：This is an improper integral because the function is not defined at x=0. We can solve this by taking the limit as the lower bound of the integral approaches 0 from the right.Step: 2 ：We can use the formula for the integral of ln(x)/x, which is 0.5*(ln(x))^2.Step: 3 ：The integral evaluates to negative infinity. This is because the function ln(x)/x approaches negative infinity as x approaches 0 from the right.Step: 4 ：Final Answer: The value of the improper integral (int_{0}^{1} frac{ln x}{x} mathrm{~d} x) is (boxed{-infty}).

Evaluate the improper integral $\int_{0}^{1} \frac{\ln x}{x} \mathrm{~d} x$

Answer

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