为什么（sinx）^2乘（cosx）^2等于（sinx）^2减（sinx）^4？请附图 数学（sinx）^2-（cosx）^2/（sinx）^4+（...
\u6c42\u89e3\u222b\uff08cosx\uff09^2/\uff08sinx\uff09^4 dx
\u7b54\u6848\u5982\u56fe
\u539f\u5f0f=-\u222b\uff08cos2x)dx/{[(sinx)^2+(cosx)^2]-2(sinxcosx)^2}
=-\u222b\uff08cos2x)dx[1-(1/2)\uff08sin2x)^2]]
=-2\u222b\uff08cos2x)dx[2-(sin2x)^2]
=-\u222bd(sin2x)/[2-(sin2x}^2]
\u4ee4sin2x=u,
\u539f\u5f0f=-\u222bdu/(2-u^2)
=-1/(2\u221a2\uff09\u222b[1/\uff08\u221a2-u)+1/(\u221a2+u)]du
=\uff08\u221a2/4\uff09ln|\u221a2-u|-(\u221a2/4)ln(\u221a2+u|+C
=\uff08\u221a2/4\uff09ln|(\u221a2-sin2x)/\uff08\u221a2+sin2x)|+C.
（sinx)^2(cosx)^2 = (sinx)^2[1-(sinx)^2]=(sinx)^2-(sinx)^4
绛旓細鍙互鐢ㄧ瓑浠锋棤绌峰皬浠ｆ崲锛sinx^2~x^2锛sinxsinx~x^2 鎵浠ユ瀬闄愪负1
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