This is essentially the same question you asked in "http://mathhelpforum.com/calculus/221129-equations-trigonometric-functions.html". Please do not post the same question twice.
Please explain the method of integrating trigonometric functions which have a power to them like cos^{54} (x). I have heard that only even powered trig functions have a method for solving them. For odd powered trig functions you have to break them down into a product like to integrate cos^{3} (x). You will write cos(x) times cos^{2}(x) And use the formula of integration by parts. Is that correct?
And what about trig functions with a power positive but less than one like cos^{0.8}(x).
What about trig functions like cos^{2.8}(x) .
in theory, if its only an indefinite integration, you can always use the reduction formulas to reduce the powers and then integrate.
Integration by reduction formulae - Wikipedia, the free encyclopedia
the result would be terribly long in this case.
I don't think that these can be integrated by using elementary functions...at least wolfram alpha thinks so...
Integrate cos^2.8 x - Wolfram|Alpha