Integrating ln(x+1) with Integration by Parts

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Homework Help Overview

The discussion revolves around the integration of the function ln(x+1) using integration by parts. Participants are exploring various substitutions and approaches to solve the integral, while also addressing potential misunderstandings in the setup of the integration by parts formula.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Some participants suggest different choices for u and dv, questioning the original poster's selection of u = x + 1 and dv = ln(x+1) dx. Others propose using u = ln(x+1) and dv = dx instead. There are discussions about the correctness of integrating certain expressions and the steps involved in applying the integration by parts formula.

Discussion Status

The conversation is ongoing, with participants providing guidance and alternative methods. Some express confusion over the integration process, while others clarify steps and offer insights into potential mistakes. There is a recognition of different interpretations and approaches being explored without a definitive consensus on the correct method yet.

Contextual Notes

Participants are working under the constraints of a homework assignment that requires the use of integration by parts. There are indications of varying levels of understanding regarding integration techniques, particularly in the context of logarithmic functions.

  • #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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