Find the general indefinite integral.

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SUMMARY

The discussion centers on finding the general indefinite integral of the function 1/(1+x^2). The correct antiderivative is the inverse tangent function, commonly denoted as arctan or tan-1. A critical point emphasized is the importance of verifying the solution by differentiating the antiderivative to ensure it matches the original integrand. The incorrect notation tan-2 was pointed out as a common mistake.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly integration.
  • Familiarity with the notation and properties of inverse trigonometric functions.
  • Knowledge of differentiation to verify antiderivatives.
  • Experience with algebraic manipulation of rational functions.
NEXT STEPS
  • Study the properties and applications of inverse trigonometric functions, focusing on arctan.
  • Practice finding antiderivatives of various rational functions.
  • Learn techniques for verifying integrals through differentiation.
  • Explore common mistakes in calculus notation and how to avoid them.
USEFUL FOR

Students studying calculus, educators teaching integration techniques, and anyone looking to improve their understanding of antiderivatives and inverse functions.

phillyolly
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Homework Statement



Hi! Can anyone check if I got the right answer?


The Attempt at a Solution

 

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Looks fine, except the antiderivative of 1/(1+x^2) is inverse tangent, or arctan, sometimes written tan^(-1), but tan^(-2) doesn't make much sense.
 
And whenever you find an antiderivative, it's a good idea to check your work. If you take the derivative of your answer, you should get the integrand.
 

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