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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!

Mathematics
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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
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.
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

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Some of the examples you linked seems good, thank you!
lol, sorry; didnt read it properly!!
Btw, the example is solved by triple variable substitutionand gives quite a neat answer ;)

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