I've learned before that integrals such as int(sec^4)xdx or (sec^2)x(tan^2)xdx have solutions that, while not completely obvious, can be solved with a number of u substitutions and/or integration by parts. But how about integrals of trigonometric functions raised to arbitrarily large exponents, like (sec^18)x(cot^5)xdx?
I've learned before that integrals such as int(sec^4)xdx or (sec^2)x(tan^2)xdx have solutions that, while not completely obvious, can be solved with a number of u substitutions and/or integration by parts. But how about integrals of trigonometric functions raised to arbitrarily large exponents, like (sec^18)x(cot^5)xdx?