积分(sinx)^4(cosx)^4dx

∫(sinx)^4(cosx)^4dx=∫(sinxcosx)^4dx=∫(1/2sin2x)^4dx = 1/16∫(sin2x)^4dx
=1/16∫[(sin2x)^2]^2dx
(sin2x)^2 = (1-cos4x)/2带入得到
=1/64∫[(1-cos4x)]^2dx
= 1/64∫[(1-2cos4x+(cos4x)^2)]dx
(cos4x)^2= (1+cos8x)/2带入得到
= 1/64∫[(3/2-2cos4x+1/2 cos8x)]dx
= 1/64∫3/2dx -1/32∫cos4xdx + 1/128∫cos8xdx
这下会了吧?