Integrating arctan(y) with respect to x

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    Dx Integrate
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Discussion Overview

The discussion revolves around the integration of the function M(x,y) = x + arctan(y) with respect to x, specifically focusing on the integration of the arctan(y) term. The context includes mathematical reasoning related to differential equations.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks for the steps to integrate arctan(y) with respect to x.
  • Another participant suggests that the integral should be arctan(y) * x.
  • A third participant agrees, stating that since arctan(y) is a function of y and does not depend on x, it can be treated as a constant during integration.
  • A later reply reiterates the previous point, adding a constant of integration.

Areas of Agreement / Disagreement

Participants generally agree that arctan(y) can be treated as a constant with respect to x during integration, but the discussion does not explore any alternative viewpoints or unresolved issues.

lolallday
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Hi,

Part of solving a differential equation involves integrating M(x,y) with respect to x, where M(x,y) = x + tan-1(y). What are the steps to integrating the arctan portion?

\int tan-1(y) dx

Thank you.
 
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If I'm not mistaken, it should just be tan-1(y) * x
 
welcome to pf!

hi lolallday! welcome to pf! :wink:

i agree with m1ke_ :smile: …

a function of y does not depend on x, so it integrates (and differentiates) as a constant
 
m1ke_ said:
If I'm not mistaken, it should just be tan-1(y) * x

+ C :-p
 

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