第1个回答 2013-12-14
解:
设x=asint,t=arcsin(x/a),dx=acostdt,a^2-x^2=a^2cos^2t
原式=
∫(acost/a^4sin^4t)acostdt
=1/a^2∫cot^2tcsc^2tdt
=-1/a^2∫cot^2tdcot
=(-1/3a^2)cos^3t
=(-1/3a^2)cos^3(arcsin(x/a))
=(-1/3a^2)(1-(x/a)^2)^(3/2)
设x=asint,t=arcsin(x/a),dx=acostdt,a^2-x^2=a^2cos^2t
原式=
∫(acost/a^4sin^4t)acostdt
=1/a^2∫cot^2tcsc^2tdt
=-1/a^2∫cot^2tdcot
=(-1/3a^2)cos^3t
=(-1/3a^2)cos^3(arcsin(x/a))
=(-1/3a^2)(1-(x/a)^2)^(3/2)
第2个回答 2013-12-14
还没学到这里来
相似回答