How Can I Integrate sqrt(2+2sin(x))?

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Discussion Overview

The discussion revolves around the integration of the expression sqrt(2+2sin(x)). Participants are exploring various methods and substitutions to tackle the integral, focusing on mathematical reasoning and transformations.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in integrating sqrt(2+2sin(x)) and seeks assistance.
  • Another suggests rewriting the expression as sqrt(2)*sqrt(1+sin(x)) as a potential starting point.
  • A participant proposes a substitution using \tan\frac{x}{2}=t to simplify the integration process.
  • Further clarification is requested regarding the substitution and its application.
  • Another participant suggests transforming the integral into the form \sqrt{2}\int \sqrt{1+\sin x} \ dx with the substitution x=2\arctan t.
  • A different approach is introduced, where sqrt(1+sin(x)) is expressed as [(cos(x))^2]/[sqrt(1-sin(x))], inviting exploration of this transformation.

Areas of Agreement / Disagreement

Participants present multiple approaches and suggestions without reaching a consensus on a single method for integration. The discussion remains unresolved with various competing ideas.

Contextual Notes

Some participants' suggestions depend on specific substitutions and transformations that may not be universally applicable without further context or assumptions.

lostinhere
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I'm having trouble with this. Can anyone help me integrate

sqrt(2+2sin(x))

??

Thanks
 
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lostinhere said:
sqrt(2+2sin(x))
Can you out it into a different form first?

The Bob (2004 ©)
 
Other than
sqrt(2)*sqrt(1+sin(x))

I'm stuck
 
HINT:Make the substitution

[tex]\tan\frac{x}{2}=t[/tex]

Daniel.
 
Can you be more specific please?
 
Transform the integral (make a change of variable).

[tex]\sqrt{2}\int \sqrt{1+\sin x} \ dx[/tex]

[tex]x=2\arctan t[/tex]

Daniel.
 
hello there

sqrt[1+sinx]=[(cosx)^2]/[sqrt[1-sinx]]

see what you could do with that if it helps

steven
 

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