∫(0,1)x²/(1+x²)³dx

问题描述:

∫(0,1)x²/(1+x²)³dx

建议换元,令x=tany
剩下的自己算就行了

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(...