Antiderivative of anti-trigs(arctan)

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SUMMARY

The discussion focuses on finding the antiderivative of the function arctan(x)/(1+x^2). A participant attempted to simplify the integral by pulling out arctan(x) but encountered confusion regarding the presence of a 1/2 coefficient in the final answer. The correct approach involves using u-substitution to properly evaluate the integral, as constants can be factored out, but functions like arctan(x) cannot.

PREREQUISITES
  • Understanding of antiderivatives and integration techniques
  • Familiarity with the arctangent function and its properties
  • Knowledge of u-substitution in calculus
  • Basic algebraic manipulation skills
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  • Study the method of u-substitution in integral calculus
  • Learn about the properties and derivatives of inverse trigonometric functions
  • Explore integration techniques for rational functions
  • Review examples of integrals involving arctan and their solutions
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Students studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of common pitfalls in evaluating antiderivatives involving inverse trigonometric functions.

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Homework Statement



arctan(x)/(1+x2). finding the antiderivative

Homework Equations



arctanx=1/1+x^2

The Attempt at a Solution



I tried pulling out arctan(x) S 1/(1+x^2) dx --> arctan^2(x)+c but the answer also has a 1/2 in front of the arctan...where'd that come from?
 
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You can't just pull out the arctan! You can only pull out constants. Try making a u-substitution.
 

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