∫sin^3xcos^3dx=∫1/8sin^32xdx
=1/8∫sin^32xdx
=1/16∫sin^32xd2x
=-1/16∫sin^22xdcos2x
=-1/16∫(1-cos^22x)dcos2x
=-1/16(cos2x-cos^32x/3)
累死我了！！！
参考资料：自己做的
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一道积分题 ∫sin^3xcos^3dx=
如果sin^3x理解为(sinx)^3 ∫sin^3xcos^3dx=∫sin^3x(1-sin^2)dsinx =∫(sinx)^3dsinx-∫(sinx)^5dsinx =(sinx)^4\/4-(sinx)^6\/6+C
一道积分题 ∫sin^3xcos^3dx=
sinx*cosx=1\/2sin2x ∫sin^3xcos^3dx=∫1\/8sin^32xdx =1\/8∫sin^32xdx =1\/16∫sin^32xd2x =-1\/16∫sin^22xdcos2x =-1\/16∫(1-cos^22x)dcos2x =-1\/16(cos2x-cos^32x\/3)累死我了！！！参考资料：自己做的
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