∫(sinx)^3d(cosx)^3 = -3∫(sinx)^4(cosx)^2dx
= (-3/8)∫ 2(sinx)^2 [4(sinx)^2(cosx)^2] dx
= (-3/8)∫ (1-cos2x) (sin2x)^2 dx
= (-3/8)∫(sin2x)^2dx + (3/8)∫cos2x(sin2x)^2dx
= (-3/16)∫(1-cos4x)dx + (3/16)∫(sin2x)^2dsin2x
= -3x/16 + (3/64)sin4x + (1/16)(sin2x)^3 + C
= (-3/8)∫ 2(sinx)^2 [4(sinx)^2(cosx)^2] dx
= (-3/8)∫ (1-cos2x) (sin2x)^2 dx
= (-3/8)∫(sin2x)^2dx + (3/8)∫cos2x(sin2x)^2dx
= (-3/16)∫(1-cos4x)dx + (3/16)∫(sin2x)^2dsin2x
= -3x/16 + (3/64)sin4x + (1/16)(sin2x)^3 + C
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第1个回答 2020-03-04
方法如下图所示，
请认真查看，
祝学习愉快：
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