Integration with Sines and Cosines

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Homework Statement



\intsinxcosx/sin^4x+cos^4x


Homework Equations



sin^2x=1/2-1/2cos(2x)

cos^2x=1/2+1/2cos(2x)

sinxcosx=1/2sin(2x)

The Attempt at a Solution



\int1/2 sin(2x)/(1/2-1/2cos(2x))^2 + (1/2 + 1/2cos(2x))^2

\int1/2 sin(2x)/1/2 + 1/2cos^2(2x)

...?

Am I on the right track?
 
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Hi Ayesh! :smile:

(have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)

Ayesh said:
… \int1/2 sin(2x)/1/2 + 1/2cos^2(2x)

...?

Am I on the right track?

Yes, that's fine.

(though it would have been quicker to notice that the original denominator is almost the square of cos2x + sin2x :wink:)

And you should be able to integrate it immediately. :smile:
 
Thank you!
 
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Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...

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