令arcsin√x=t
√x=sint
x=sin^2 t
dx=dsin^2 t
原式=∫tdsin^2 t
=tsin^2 t-∫sin^2 t dt
=tsin^2 t-∫(1-cos2t)dt/2
= tsin^2 t-1/2∫dt+1/2∫cos2tdt
= tsin^2 t-t/2+1/4∫cos2td2t
= tsin^2 t-t/2+sin2t/4+C
=xarcsin√x-arcsin√x/2+2sintcost/4+C
=xarcsin√x-arcsin√x/2+√xcosarcsin√x/2+C
=xarcsin√x-arcsin√x/2+√x√(1-sin^2arcsin√x)/2+C
=xarcsin√x-arcsin√x/2+√x√(1-x)/2+C
代值=π/2-π/6=π/3
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