amycaisha
幼苗
共回答了23个问题采纳率:91.3% 举报
先化简,令t=arcsin(x) ,则 x=sin(t) arccos(x)=π/2 -t 原式=∫t(π/2 -t)dsin(t)=t(π/2 -t)sin(t) -∫ sint d(t(π/2 -t))=t(π/2 -t)sin(t) -∫ (π/2-2t)sint dt=t(π/2 -t)sin(t) +∫ (π/2-2t) dcos(t)=t(π/2 -t)sin(t) + (π/2-2t) cos(t)-∫cos(t)d (π/2-2t)=t(π/2 -t)sin(t) + (π/2-2t) cos(t)+∫2cos(t)dt=t(π/2 -t)sin(t) + (π/2-2t) cos(t)+2sin(t)+C=arcsin(x)arccos(x)x+(arccos(x)-arcsin(x))√(1-x²)+2arcsin(x)+C
1年前
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