Integral of Function: Solve Here!

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SUMMARY

The integral of the specified function is identified as an elliptic integral. Users are advised to familiarize themselves with complete elliptic integrals before attempting to solve the problem. The solution is expressed as sqrt(2)xE(x|0.5), where E(x) denotes the elliptic integral of the second kind. For further assistance, the discussion references Wolfram Alpha and a related post on Physics Forums.

PREREQUISITES
  • Understanding of elliptic integrals
  • Familiarity with trigonometric identities, specifically \(\cos 2x\) and \(\cos^2 x\)
  • Basic knowledge of integral calculus
  • Experience using Wolfram Alpha for mathematical computations
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  • Study complete elliptic integrals and their properties
  • Learn how to compute elliptic integrals of the second kind using mathematical software
  • Explore trigonometric identities and their applications in integration
  • Review related discussions on Physics Forums for additional context and examples
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Students and professionals in mathematics, particularly those focused on integral calculus and elliptic integrals, as well as anyone seeking to enhance their problem-solving skills in advanced calculus topics.

endoparasite
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hi every one ,
i want to find the integral of function given in the attachment.Please help!
 

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try using, \cos 2x=\cos^2x-\sin^2x

and \cos^2x/2=\sqrt{\frac{1+\cos x}{2}}
 
there was another post on this here: https://www.physicsforums.com/showthread.php?t=444905

but to reiterate, it is an elliptic integral. learn what complete elliptic integrals are before you attempt this problem. however, if you do know what elliptic integrals are, you would know that it would be sqrt(2)xE(x|0.5) where E(x) is an elliptic integral of the second kind.
 

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