令：x=sint
∫x^2dx/√1-x^2
=∫sin^2t costdt /cost
=∫sin^2t dt
=1/2∫(1-cos2t)dt
=t/2-sin2t/4 +c
=t/2-sintcost/2+c
=1/2[arcsinx - x√1-x^2]+c
∫x^2dx/√1-x^2
=∫sin^2t costdt /cost
=∫sin^2t dt
=1/2∫(1-cos2t)dt
=t/2-sin2t/4 +c
=t/2-sintcost/2+c
=1/2[arcsinx - x√1-x^2]+c
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第1个回答 2010-08-25
令x=sint，t=arcsinx
∫(sint)^2dx
=1/2∫1-cos2t dt
=t/2-sin2t/4+c
则∫x^2dx/√1-x^2=arcsinx/2-(x√1-x^2)/2+c
∫(sint)^2dx
=1/2∫1-cos2t dt
=t/2-sin2t/4+c
则∫x^2dx/√1-x^2=arcsinx/2-(x√1-x^2)/2+c
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