∫(-1,0) 1/[(x+1)^(1/3)+2]dx令t=(x+1)^(1/3)+2，则x=(t-2)^3-1，dx=3(t-2)^2dt原式=∫(2,3) (1/t)*3(t-2)^2dt=3*∫(2,3) (t-4+4/t)dt=3*[(t^2)/2-4t+4ln|t|]|(2,3)=3*(9/2-12+4ln3-2+8-4ln2)=12ln(3/2)-9/2
详情如图所示
有任何疑惑，欢迎追问
