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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
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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slaaibakBest ResponseYou've already chosen the best response.1
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

Mimi_x3Best ResponseYou've already chosen the best response.0
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

frxBest ResponseYou've already chosen the best response.0
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

frxBest ResponseYou've already chosen the best response.0
Some of the examples you linked seems good, thank you!
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.0
lol, sorry; didnt read it properly!!
 one year ago

frxBest ResponseYou've already chosen the best response.0
Btw, the example is solved by triple variable substitutionand gives quite a neat answer ;)
 one year ago
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