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frx Group Title

Have been looking for exercises similar to this one \[\int\limits_{}^{} \frac{ \sin2\theta }{ \cos ^{2}\theta+6\cos \theta+10 }d \theta \] without any real success. I know this isn't mainly the reason for questions in subclass Mathematics but it seems most likely for anyone here to know good resources for these kinds of exercises. Thanks in advance!

  • one year ago
  • one year ago

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  1. slaaibak Group Title
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    Hmm. Not sure if this really helps, but try: http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html also look at calculus textbooks, like thomas, stewart, etc

    • one year ago
  2. Mimi_x3 Group Title
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    According to wolfram: \[\int\limits\frac{2sinxcosx}{\cos^{2}x+6cosx+10} \] \[\int\limits\frac{\sin(2x)}{\cos^{2}(x)+6\cos(x)+10} = \int\limits\frac{2\sin(2x)}{12cosx+\cos(2x)+21} =2\int\limits\frac{\sin(2x)}{12\cos(x)+\cos(2x)+21} \] Not going to look nice though. :/ I can't think of a better method; needs more thinnking.

    • one year ago
  3. frx Group Title
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    Hehe, I've already solved the one I gave as example, the question was whether anyone knew any good resource for more "of the same type"-exercises. Thanks anyways :P

    • one year ago
  4. frx Group Title
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    Some of the examples you linked seems good, thank you!

    • one year ago
  5. Mimi_x3 Group Title
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    lol, sorry; didnt read it properly!!

    • one year ago
  6. frx Group Title
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    Btw, the example is solved by triple variable substitutionand gives quite a neat answer ;)

    • one year ago
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