Need help understanding proof of natural log integrals

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SUMMARY

The discussion focuses on proving the identity related to the natural logarithm integrals, specifically the integral of 1/t from 1 to 1/x. The user seeks guidance on how to approach proofs, emphasizing the importance of starting with one side of the equation and manipulating it to match the other side. A substitution method using u = xt is suggested to facilitate the proof process. The conversation highlights the significance of understanding foundational calculus concepts, particularly the product rule.

PREREQUISITES
  • Understanding of integral calculus, specifically natural logarithm integrals.
  • Familiarity with substitution methods in integration.
  • Knowledge of the product rule in calculus.
  • Basic proof techniques in mathematics.
NEXT STEPS
  • Study the proof of the product rule in calculus.
  • Learn about substitution techniques in integral calculus.
  • Explore the properties of natural logarithms and their integrals.
  • Practice solving various integral proofs to enhance proof skills.
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Students studying calculus, mathematics enthusiasts, and anyone looking to improve their proof-writing skills in the context of natural logarithm integrals.

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[PLAIN]http://img31.imageshack.us/img31/9004/screenshot20111117at720.png

Proofs always get to me for some reason. It's like other problems I can do, but when it comes to proofs I don't know what to put. Can anyone show me steps?

Thank you
 
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Here you need to prove an identity. So, start with one side of the equation and arrive at something. Then start messing with the other side and try to reach that same something.

If you have already proved the product rule, this little trick may come in handy:

\frac{1}{x}=\frac{1}{x}^2x[\tex]
 
You want to look at
\int_1^{1/x} \frac{1}{t}dt

Try the substitution u= xt.
 

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