sin ^3 (x)的积分怎么算

∫ 1/(sin x)^3 dx
=∫ (cscx)^3 dx
=-∫ cscx d(cotx)
=-cscxcotx+∫ cotx d(cscx)
=-cscxcotx-∫ (cotx)^2(cscx)dx
=-cscxcotx-∫ [(cscx)^2-1](cscx)dx
=-cscxcotx-∫ (cscx)^3dx+∫(cscx)dx
=-cscxcotx-∫ (cscx)^3dx+ln|cscx-cotx|
将-∫ (cscx)^3dx移到等式左边与左边合并,除去系数得
∫ 1/(sin x)^3 dx=-1/2cscxcotx+1/2ln|cscx-cotx|+C

∫sin ^3 xdx
=-∫sin ^2 xdcosx
=-∫(1-cos ^2 x)dcosx
=-cosx+cos^3x/3+C

原式=∫(sinx*sin²xdx
=∫(sinx[(1-cos2x)/2]dx
=1/2∫(sinx-sinxcos2x)dx
=1/2∫(sinx-sinxcos2x)dx
=1/2∫[sinx-1/2(sin3x)-sinx)]dx
=1/2∫(3/2*sinx-1/2*sin3x)dx
=-1/4*cosx+1/12*cos3x+C