This is not A Homework problem, I am just wondering.

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SUMMARY

The integral of ln|x| can be calculated using integration by parts. By setting u = ln(x) and v = x, the integral is expressed as ∫ ln(x) dx = x ln(x) - ∫ x (1/x) dx. This simplifies to x ln(x) - x + C, where C is the constant of integration. The discussion highlights the effectiveness of integration by parts in solving this integral, demonstrating a clear application of the technique.

PREREQUISITES
  • Understanding of integration techniques, specifically integration by parts.
  • Familiarity with natural logarithms and their properties.
  • Basic knowledge of calculus, particularly integral calculus.
  • Ability to manipulate algebraic expressions involving logarithmic functions.
NEXT STEPS
  • Study the derivation and applications of the integration by parts formula.
  • Explore other integrals involving logarithmic functions, such as ∫ ln(x^2) dx.
  • Learn about the properties of logarithmic functions and their derivatives.
  • Practice solving integrals using different techniques, including substitution and partial fractions.
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Students and educators in calculus, mathematicians, and anyone looking to strengthen their understanding of integration techniques and logarithmic functions.

bmed90
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What would the integral of ln|x| be.
 
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Applying integration by parts which states

[tex]\int u\frac{dv}{dx}\,dx = uv - \int v \frac{du}{dx}\,dx[/tex]
[tex]u=ln(x)[/tex] and [tex]v=x[/tex] So [tex]\int ln(x)\,dx = xln(x) - \int x\frac{1}{x}\,dx = xln(x)-x+c[/tex]
 
I wouldn't have thought to use parts. Thanks, I appreciate it
 

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