How Do You Derive the Integral of 1/(x^2 + a^2)?

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Homework Help Overview

The discussion revolves around deriving the integral of the function 1/(x^2 + a^2), which falls under the subject area of calculus, specifically integral calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the idea of showing that the derivative of a proposed antiderivative equals the original function. There is mention of using substitution methods to approach the integral, with one participant suggesting a specific substitution involving the tangent function.

Discussion Status

The discussion is active, with participants sharing different perspectives on how to approach the integral. Some guidance has been offered regarding the use of substitution, but there is no explicit consensus on the method to be used.

Contextual Notes

There is a mention of homework constraints that require participants to work through the integral using specific techniques rather than simply verifying the result through differentiation.

Kalie
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Yeah this one is good...

Derive the following:

int(1/(x^2 + a^2)dx = 1/a*arctan(x/a) + C

any idea how I would derive this thing?
Cause I'm totally lost...
 
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Well do you agree that if you show that the derivative of 1/a*arctan(x/a) + C is 1/(x^2 + a^2, then you will have attained your goal?
 
fundamental theorem of calculus
 
no he actually wants us to plow thorugh the intregal using subsitution and stuff and then somehow end up at the answer
 
use the substitution [tex]x = a\tan \theta[/tex]
 

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