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 cos54 (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 cos3 (x). You will write cos(x) times cos2(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 cos0.8(x).
What about trig functions like cos2.8(x) .
Integration by reduction formulae - Wikipedia, the free encyclopedia
the result would be terribly long in this case.
Integrate cos^2.8 x - Wolfram|Alpha