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What is the answer to this trig substitution problem (x^4)?
I see. How do we integrate this expression now?
We can use the power reduction formula for cosine: cos^n(theta) = (1/2^n)(sum of k=0 to n) (n choose k) cos((n-2k)theta). Applying this formula to our integral, we get: 8integral of [1/8 + 1/4cos(2theta) - 3/8cos(4theta) + 1/4cos(6theta) - 1/8cos(8theta)] d(theta).