Integrating ln(x+1) with Integration by Parts

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SUMMARY

The forum discussion focuses on the integration of the function ln(x+1) using the method of integration by parts. Participants clarify the correct assignments for u and dv, with the consensus being to let u = ln(x+1) and dv = dx. The correct integral is derived as (x+1)ln(x+1) - (x+1) + C, and participants emphasize the importance of correctly applying the integration by parts formula: ∫u dv = uv - ∫v du. Additionally, resources for further practice in integration techniques are shared.

PREREQUISITES
  • Understanding of integration by parts formula
  • Familiarity with basic calculus concepts
  • Knowledge of logarithmic functions and their properties
  • Ability to differentiate and integrate basic functions
NEXT STEPS
  • Practice integration by parts with various functions
  • Explore tabular integration techniques for simplifying integration by parts
  • Study the properties of logarithmic functions in calculus
  • Review calculus textbooks such as Stewart's Calculus for additional practice problems
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques, as well as educators seeking to enhance their teaching methods in integration by parts.

  • #31
rootX said:
which book you are using?
Most calculus books have like +200 integration questions ... You can always go to the library and find Stewart etc.
http://www.stewartcalculus.com/

I remember looking for some practice sites but wasn't really successful.

And, you don't need to know the answers for all the questions you solve.

hmm..rootx..do we have a special formula to factorize out for cubic equation?for example (x^3 + 27)?
 
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  • #32
Yes... you should know that formula and if you do not at the calculus level you should know how to figure it out :)

Note that if f(x) = x^3 + 27 then f(-3) = 0 hence -3 is a root of that equation and therefore (x + 3) divides x^3 + 27. Now do division.
 

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