do any1 knows a simple method to integrate $\displaystyle sin^ 8x dx $ obviously without expanding..........
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The usual method (for an even power) is to make repeated use of the formulae $\displaystyle \sin^2A = \frac{1}{2}(1-\cos2A),$ $\displaystyle \cos^2A = \frac{1}{2}(1+\cos2A)$ to reduce the power(s) down to 1.
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