How to integrate int -1/(x^2 +1)^2 dx

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    Dx Integrate
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Homework Help Overview

The discussion revolves around the integral of the function \(-\frac{1}{(x^2 + 1)^2}\). Participants are exploring methods to approach this integral within the context of calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster expresses difficulty in progressing with the integral and seeks hints. Some participants suggest various techniques, including differentiation of the arctangent function and manipulating the numerator. Another participant proposes a substitution involving the tangent function.

Discussion Status

The discussion is active, with participants offering hints and suggestions without reaching a consensus on a specific method. Multiple approaches are being explored, indicating a collaborative effort to understand the problem better.

Contextual Notes

There is a mention of an initial mistake in the problem setup by one participant, which may affect the clarity of the discussion. The original poster's request for hints suggests a learning environment where guidance is sought rather than direct solutions.

cscott
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Homework Statement



Find the following intergral...

Homework Equations



\int{\frac{-1}{(x^2+1)^2}dx}

The Attempt at a Solution



I can't get anywhere with this... any hints?
 
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sorry rushed the problem and did it wrong
 
Last edited:
hint:

\frac{d}{{dx}}{\arctan{x}} = \frac{1}{x^2 +1}
 
Last edited:
Try adding and subtracting x^2 in the numerator.
 
Make the substitution x=\tan t. You'll eventually get \int \cos^2 t \ dt which is easy to do.

Daniel.
 

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