I forgot how to do this integration Help

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Homework Help Overview

The discussion revolves around an integration problem where the original poster expresses uncertainty about the methods available for solving it. The subject area is calculus, specifically focusing on integration techniques.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to recall different methods for integration, mentioning a preference for a trigonometric approach while also seeking alternatives. Some participants suggest specific substitutions and methods, while others question the necessity of exploring additional techniques if one method appears sufficient.

Discussion Status

The discussion is ongoing, with various methods being proposed, including trigonometric substitution and hyperbolic functions. Participants are exploring different approaches without reaching a consensus on the best method to use.

Contextual Notes

The original poster indicates a lack of memory regarding certain integration techniques, which may affect the discussion. There is also an implicit constraint regarding the need for clarity in the methods discussed, as the poster seeks guidance rather than complete solutions.

Karmerlo
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Homework Statement



Do the integration

Homework Equations



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The Attempt at a Solution



I forgot how to do this integration with another method. I think I can do it through Trigonometric Method. But I remember that there is still another way to do it without using Trigonometric Method. Anyone can show me steps to do it? Thanks.
 
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Well, for the trig method you would use the substitution let x = ytan(u)
If that gets you the right answer then why bother with another method. I can't think of a different method right now that would work.
 
Take the derivative of \displaystyle \frac{x}{y^2\sqrt{x^2+y^2}}\,, treating y as a constant, of course. Then see if you can reverse the process.
 
Try a substitution x=y \sinh t. The resulting integration will be trivial.
 

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