求不定积分∫sin四次方xdx
问题描述：
求不定积分∫sin四次方xdx
答
∫(sinx)^4dx=∫(sinx)^2*(sinx)^2dx=∫((1/2)*(1-cos2x))*((1/2)*(1-cos2x))dx
=∫(1/4)*(1+(cos2x)^2-2cos2x)dx=(1/4)x+(1/4)∫(cos2x)^2dx-(1/4)sin2x
=(1/4)x+(1/8)∫(cos4x+1)dx-(1/4)sin2x
=(3/8)x+(1/32)sin4x-(1/4)sin2x+c