Help with trigonometric integral

  • Thread starter miglo
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  • #1
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Homework Statement


[tex]\int_{\frac{5\pi}{6}}^{\pi}\frac{\cos^{4}x}{\sqrt{1-\sin{x}}}dx[/tex]

Homework Equations


[tex]\cos^{2}x=\frac{1+\cos{2x}}{2}[/tex]


The Attempt at a Solution


i used the above equation, then expanded it all out and multiplied by the denominator and hoped i would then be able to do a simple substitution that would give me an antiderivative after integrating but that hasn't been working for me
any ideas?
 

Answers and Replies

  • #2
Hootenanny
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Homework Statement


[tex]\int_{\frac{5\pi}{6}}^{\pi}\frac{\cos^{4}x}{\sqrt{1-\sin{x}}}dx[/tex]

Homework Equations


[tex]\cos^{2}x=\frac{1+\cos{2x}}{2}[/tex]


The Attempt at a Solution


i used the above equation, then expanded it all out and multiplied by the denominator and hoped i would then be able to do a simple substitution that would give me an antiderivative after integrating but that hasn't been working for me
any ideas?
A relatively straightforward method involves a series of substitutions. I would start with [itex]u=1-\sin x[/itex]
 

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