Understanding the Integration of 1/(x^2+d^2)^1/2: A Step-by-Step Explanation

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Homework Help Overview

The discussion revolves around finding the integral of the function 1/(x^2+d^2)^(1/2) with respect to dx, where d is a constant. The original poster expresses confusion regarding the solution provided in their textbook, which differs from their own attempt.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants suggest various substitutions, including x = d.sec(u) and x = d.tan(u), to simplify the integration process. There is also a mention of potential confusion arising from the choice of the constant d.

Discussion Status

The discussion is ongoing, with participants exploring different substitution methods to approach the integral. There is no explicit consensus yet, but several suggestions have been made to guide the original poster's understanding.

Contextual Notes

There is a note regarding the choice of the constant d, indicating that it may lead to confusion during differentiation. This highlights a consideration of clarity in variable selection within the context of the problem.

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Homework Statement




To find the INTEGRAL of 1/(x^2+d^2)^1/2 integrated with respect to dx.
d is a constant

I tried to write it as :

ln (x^2+ d^2)^1/2

but my book gives an answer of

ln { x + (x^2+ d^2)^1/2 }

i don't understand how. Can you please explain it step by step. Clearly please.
 
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how about starting with the subtitution x = d.sec(u)?
 
Even better, use the substitution:

<br /> x=d\sinh u<br />
 
Last edited:
actually i meant x = d.tan(u), which makes more sense... but i'd still try huntmat's suggestion
 
also d is a bad constant to use when you're differentiating as you may get confused, something like a or s would be better
 

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