不定積分:sinx^3cosx^2

不定積分:sinx^3cosx^2


∫sinx^3cosx^2dx
=-∫sin^2xcos^2xdcosx
=-∫(1-cos^2x)cos^2xdcosx
=-∫(-cos^4x+cos^2x)dcosx
=(1/5)cos^5x-(1/3)cos^3x+C



sinx^3cosx^2的不定積分


∫sinx^3cosx^2dx
=-∫sin^2xcos^2xdcosx
=-∫(1-cos^2x)cos^2xdcosx
=-∫(-cos^4x+cos^2x)dcosx
=(1/5)cos^5x-(1/3)cos^3x+C



求不定積分:∫(sinx)^2dx


∫sin²;xdx=1/2∫(1-cos2x)dx=1/2(x-∫cos2xdx)=1/2(x-1/2∫cos2xd2x)=1/2(x-1/2sin2x)=x/2-(sin2x)/4驗算:x/2-(sin2x)/4 '=1/2-2/4 cos2x=1/2-1/2(cos²;x-sin²;x)=1/2(1-cos²;x+sin²;x)=1/…