Variant of inverse tangent derivative

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SUMMARY

The discussion focuses on calculating the integral of the function 1/(u^2+4) using the derivative of the inverse tangent function. The participant recognizes that the derivative of the inverse tangent function is 1/(x^2+1) and seeks to apply this knowledge to the given integral. The key insight is to manipulate the expression by factoring out constants to align it with the standard form of the inverse tangent derivative.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with the derivative of the inverse tangent function.
  • Knowledge of algebraic manipulation of expressions.
  • Basic concepts of trigonometric identities.
NEXT STEPS
  • Learn how to integrate functions of the form 1/(u^2+a^2).
  • Study the proof of the derivative of the inverse tangent function in detail.
  • Explore techniques for algebraic manipulation in calculus.
  • Investigate the relationship between trigonometric functions and their inverses.
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques and the properties of inverse trigonometric functions.

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Homework Statement


1/(u^2+4)


Homework Equations





The Attempt at a Solution



I know that 1/(x^2+1) is the derivative of the inverse tangent function, and that is proved by using tany = x, derivative of both sides with secx=(1+tan^2x) and tan^2x = x^2.

I don't know how to use the proof of the inverse tangent derivative to calculate the integral of 1/(u^2+4). Am I approaching this in an incorrect way?
 
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Think about how you can turn that 4 into a 1 without changing the value of the whole expression.
 

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