Question

∫dx/√(x^2+1)^3=??

Answer 1

令x=tant dx=sec^2tdt
原式=∫sec^2tdt/sec^3t
=∫costdt
=sint+C
=sin(arctanx)+C
=x/√(x^2+1)+C

Answer 2

let
x = tany
dx = (secy)^2 dy
∫dx/√(x^2+1)^3
= ∫cosy dy
= siny + C
= x/√(1+x^2) + C