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(...