数学（sinx）^2-（cosx）^2/（sinx）^4+（cosx）^4的积分

[(sinx)^2-(cosx)^2]/[sinx^4+cosx^4]
=-cos2x/[(sinx^2+cosx^2)^2-2sinx^2cosx^2]
=-cos2x/1-(sin2x)^2/2
∫[(sinx)^2-(cosx)^2]dx/[sinx^4+cosx^4]
=∫-cos2xdx/[1-(sin2x)^2/2]
=-∫dsin2x/(2-(sin2x)^2)
=[-1/(2√2)]∫(√2+sin2x+√2-sin2x)dsin2x/[2-(sin2x)^2]
=(-1/2√2)ln|(√2+sin2x)/(√2-sin2x)|+C

M=∫(x(cosx)^4)dx = 0 奇函数在对称区间上的定积分 N=∫ (x^2(sinx)+(cosx)^4) dx = ∫ (cosx)^4 dx > 0 P=∫(x^2(sinx)^3-(

原式=-∫（cos2x)dx/{[(sinx)^2+(cosx)^2]-2(sinxcosx)^2}
=-∫（cos2x)dx[1-(1/2)（sin2x)^2]]
=-2∫（cos2x)dx[2-(sin2x)^2]
=-∫d(sin2x)/[2-(sin2x}^2]
令sin2x=u,
原式=-∫du/(2-u^2)
=-1/(2√2）∫[1/（...