what is the quick way of doing single integrals of the form:(adsbygoogle = window.adsbygoogle || []).push({});

*integral* (sinx)^n (cosx)^m dx

where n and m are just integers. These kind of integrals come up all the time in vector calculus and they take me ages to do. Is there a general method of doing them or a few common integrals i could learn? I end up having to apply about 3 trig identites and then sorting out the mess of resulting sinxs, cosx, cos2x etc

an eg would be

*integral* cosx (sinx)^2 dx

I would do this by using (sinx)^2 + (cosx)^2 = 1

then cos^2= 1/2(1 +cos2A)

then cosCcosD=1/2(cos(C+D) + cos(C-D))

Which takes about a side and a half of a4. There must be a simpler way (substitutions, change of variables?)

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# Quick integral question

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