令x=tant,则t=arctanx,dx=sec²tdt
∫x/√(1+x²)dx
=∫tant/sect*sec²tdt
=∫tantsectdt
=∫sint/cos²tdt
=-∫1/cos²td(cost)
=1/cost+C
=sect+C
=√(1+tant²)+C
=√(1+x²)+C