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) .