What Substitution Should Be Used to Solve ∫(1+x)/(1+x^2) dx?

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Homework Help Overview

The discussion revolves around the integral ∫(1+x)/(1+x^2) dx, which falls under the subject area of calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore various substitution methods, including u-substitution with different expressions. There is a suggestion to split the integral into two parts for separate analysis, and questions arise regarding the appropriateness of specific substitutions.

Discussion Status

The discussion is active, with participants providing different perspectives on how to approach the integral. Some guidance has been offered regarding splitting the integral and considering different substitutions for each part, although no consensus has been reached on a single method.

Contextual Notes

Participants mention the potential need for partial fractions or polynomial long division, indicating that the problem may have multiple approaches depending on the interpretation of the integral's components.

Miike012
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∫(1+x)/(1+x^2) dx = ...

I have tryed multiple time using u substitution letting u = 1+ x... 1 + x^2... x ..x^2 but I can't get any of them to work.
 
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Not surprising. Split the integral up into 1/(1+x^2) and x/(1+x^2). You need a different substitution for each part. One is a trig sub. The other isn't. They are different.
 
is it u = 1+x^2 and u = arctan(x)?
 
got it thank you.
 
With a problem like that, either use partial fractions (if numerator power is lesser) or use polynomial long division (and then partial fractions on the remainder, if needed.)

It's always been beneficial to me.
 

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