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!

Question

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!

slaaibak · Answer

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

mimi_x3 · Answer

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.

anonymous · Answer

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

anonymous · Answer

Some of the examples you linked seems good, thank you!

mimi_x3 · Answer

lol, sorry; didnt read it properly!!

anonymous · Answer

Btw, the example is solved by triple variable substitutionand gives quite a neat answer ;)