How to Integrate a Fraction with a Square Root in the Denominator

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Homework Help Overview

The discussion revolves around the integration of a fraction involving a square root in the denominator, specifically the integral of (x^5)/((1-2x^3)^(1/2)).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants suggest different substitution methods, such as y = √(1 - 2x^3) and u = 1 - 2x^3, while discussing the implications of these substitutions on simplifying the integral.

Discussion Status

There is an ongoing exploration of substitution techniques, with participants sharing their preferences and reasoning behind their choices. Some guidance is offered regarding the nature of the help expected in the forum.

Contextual Notes

Participants emphasize the importance of showing their thought process and previous attempts to facilitate more effective assistance.

nyyfan0729
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Can somebody tell me step by step how to integrate (x^5)/((1-2x^3)^(1/2)).
 
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Have you tried the substitution [itex]y = \sqrt {1 - 2x^3 }[/itex]?
 
I don't know what you have in mind TD. I would substitute u = 1 - 2x^3, with x^3 = (1 - u)/2
 
They're essentially the same thing. But I tend to prefer TD's because it gets rid of all the messy radicals!

nyyfan0729: we're not here to do the problems for you step by step. (that's already done in your textbook and solution manual anyways) We're here to help you when you're stuck: you need to show us your thoughts on the problem, and what you've tried, so that we know where you're stuck and why.
 

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