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I was working on an integration problem, and I "simplified" the integral to the following:

$$\int \limits_0^{2\pi} (7.625+.275 \cos(4x))^{1.5} \cdot (A \cos(Nx) + B \sin(Nx)) \cdot (Z-v \cos(x)) dx$$

This integral may seem impossible (I have almost lost all hope on doing this analytically.) If anyone can suggest a approach on attacking this monster, please suggest (It doesn't matter how ugly the solution will turn up to be. I will churn it out.)

Note: Assume all values to be constants EXCEPT $x$

ATTEMPTS:

An interesting idea to solve this was to use the exponential notation to replace the trigonometric functions. An example:

$$\cos(Nx) = \frac{1}{2}(e^{Nix} + e^{-Nix})$$

This allows me to express the equation in terms of these exponent terms, which is nice because the magnitude of $e^{ix}$ is 1, making the integral a closed loop integral $$\oint$$ with the integration variable equal to one. I tried to use reverse Green's theorem, but I got stuck

Suggestions?

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# A nasty integral to compute

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