Evaluate integral ∫cos2xsin4xdx.
Attempt. Setting tanx=t, gives:
∫cos2xsin4xdx=∫11+t2(t21+t2)2dt1+t2=∫t4(1+t2)4dt,
which does not seem to be elementary.
Thank in advance for the help.
Answer
Here is to integrate economically,
cos2xsin4x=18sin22x(1−cos2x)=116−116cos4x−18sin22xcos2x
Thus,
∫cos2xsin4xdx=x16−164sin4x−148sin32x+C
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