Integral of x(ln x)^4: Steps & Solution

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Homework Help Overview

The discussion revolves around the integral of the function x(ln x)^4, with participants exploring the correctness of a proposed solution and the steps involved in finding it.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster questions the validity of their solution to the integral and expresses uncertainty about their work. Some participants suggest differentiating the proposed solution to verify its correctness. Others provide alternative results from computational tools and mention resources for future reference.

Discussion Status

The discussion is active, with participants engaging in verification methods and sharing insights. While there is no consensus on the correctness of the original poster's solution, suggestions for checking the work through differentiation and using online tools have been provided.

Contextual Notes

There is a mention of the original poster's fatigue affecting their ability to present their work clearly. Additionally, a reference to a specific website for integral solutions is noted, indicating a resource for further exploration.

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Does the integral of x(ln x)^4 =
x^2/x(ln x)^4 - x^2(ln x)^3 + 3/2 x^2 (ln x)^2 - 3/2 x^2(ln x) + 3/2 x +C ?

Or did I do something completely wrong?
Sorry I didn't show my work, it would probably take me 30 mins to type it up here.
 
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Why don't you try differentiating it and see? That's all we could do anyway, and we won't do your tedious work for you.
 
Maple gives

1/2*x^2*ln(x)^4-x^2*ln(x)^3+3/2*x^2*ln(x)^2-3/2*x^2*ln(x)+3/4*x^2+C

and, in the future, try www.integrals.com (which in this case does not give the form of the answer your looking for.)
 
LOL, i forgot about differentiating that. Damn, i was so tired after solving that my mind shut down. LOL THanks.

Thanks benorin too, my professor was telling us about some website that does that, and i forgot to write it down.
 
Last edited:

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