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# Integrate the function $\frac{\ln\left(x\right)}{x}$ from 0 to $1$

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##  Final answer to the problem

The integral diverges.

##  Step-by-step Solution 

How should I solve this problem?

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• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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We can solve the integral $\int_{0}^{1}\frac{\ln\left(x\right)}{x}dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $\ln\left(x\right)$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

$u=\ln\left(x\right)$

Learn how to solve problems step by step online.

$u=\ln\left(x\right)$

Learn how to solve problems step by step online. Integrate the function ln(x)/x from 0 to 1. We can solve the integral \int_{0}^{1}\frac{\ln\left(x\right)}{x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \ln\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify.

##  Final answer to the problem

The integral diverges.

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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