问题描述: ∫(0,1)x²/(1+x²)³dx 1个回答 分类:数学 2014-09-26 问题解答: 我来补答 设x=tant,则dx=sec²tdt∵当x=0时,t=0当x=1时,t=π/4∴∫(0,1)x²/(1+x²)³dx=∫(0,π/4)tan²t*sec²tdt/(sec²t)³=∫(0,π/4)sin²t*cos²tdt=1/4∫(0,π/4)sin²(2t)dt=1/8∫(0,π/4)[1-cos(4t)]dt=1/8[t-sin(4t)/4]|(0,π/4)=1/8[π/4-0-0+0]=π/32. 展开全文阅读