令x=tan^2t
dx=2tantsec^2tdt
x=0,t=0,x=+∞,t=π/2
原式
=∫(0,+∞) dx/√[x(x+1)^3]
=∫(0,π/2) 2tantsec^2tdt/(tant*sec^3t)
=2∫(0,π/2) costdt
=2sint(0,π/2)
=2
令x=tan^2t
dx=2tantsec^2tdt
x=0,t=0,x=+∞,t=π/2
原式
=∫(0,+∞) dx/√[x(x+1)^3]
=∫(0,π/2) 2tantsec^2tdt/(tant*sec^3t)
=2∫(0,π/2) costdt
=2sint(0,π/2)
=2