Integral (cos(x))^4 use trig identity (cos(x))^2=(1/2)*(1+cos(2x)) to reduce powers twice.
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In this trig integral (cos(x))^4, use trig identity (cos(x))^2=(1/2)*(1+cos(2x)) to reduce powers twice.
We start by splitting (cos(x))^4 into (cos(x))^2*(cos(x))^2, then we apply the identity (cos(x))^2=(1/2)*(1+cos(2x)) to reduce powers. This results in an expression containing (cos(2x))^2, which means we have to apply the identity one more time.
After using the power reducing identity twice, we arrive at an integrand for which the antiderivatives are guessable using the chain rule backwards. We write down the antiderivatives and add a +C and we're done!
