∫（上限 根号3/2,下限0）xarccosxdx

Answer 1

∫xarccosxdx=1/2∫arccosxdx^2=1/2(x^2arccosx-∫x^2darccosx)
=1/2x^2arccosx-1/2∫(-x^2)/根号（1-x^2)dx
=1/2x^2arccosx-1/2∫(1-x^2-1)/根号（1-x^2)dx
=1/2x^2arccosx-1/2∫根号（1-x^2)dx+1/2∫1/根号（1-x^2)dx
=1/2x^2arccosx-1/2[1/2arcsinx+1/2*x根号（1-x^2)]+1/2arcsinx
分别将x=根号3/2和x=0代入上式,然后相减就行了,用的就是分部积分法