1)
∫x^2*arcctgxdx（采用分部积分法）
=(1/3)∫arcctgxd(x^3)
=(1/3)[x^3*arcctgx+∫x^3/(1+x^2)dx]
=(1/3)x^3*arcctgx+(1/6)∫x^2/(1+x^2)d(x^2)
=(1/3)x^3arcctgx+(1/6)∫[(x^2+1)-1]/(1+x^2)d(x^2)
=(1/3)x^3arcctgx+(1/6)∫[1-1/(x^2+1)]d(x^2)
=(1/3)x^3arcctgx+(1/6)x^2-(1/6)∫[1/(x^2+1)]d(x^2+1)
=(1/3)x^3arcctgx+(x^2/6)-(1/6)ln(x^2+1)+C

2)
对于x^2-2x-3，它在[-1,3]上小于零，除此自外均大于零。所以：
∫<-2,3>|x^2-2x-3|dx
=∫<-2,-1>(x^2-2x-3)dx+∫<-1,3>(-x^2+2x+3)dx
=[(1/3)x^3-x^2-3x]|<-2,-1>+[(-1/3)x^3+x^2+3x]|<-1,3>
=[(-1/3)-1+3]-[(-8/3)-4+6]+[-9+9+9]-[(1/3)+1-3]
=(-1/3)+2+(8/3)-2+9-(1/3)+2
=13