[4]∫dx/(1+x^2)^3/2=x/(1+x^2)^1/2
===================================
∫dx/(1+x^2)^3/2dx=∫{2t/(1+t^2)}^3・(1+t^2)/2t^2dt
=2∫2t/(1+t^2)^2dt
1+t^2=sとおく.2tdt=ds
=2∫1/s^2ds=-2/s
t=x+(1+x^2)^1/2
s=2+2x^2+2x(1+x^2)^1/2
-2/s=-1/{1+x^2-x(1+x^2)^1/2}
(1+x^2)^2-x^2(1+x^2)=1+x^2
-2/s=-{1+x^2-x(1+x^2)^1/2}/(1+x^2)
=x/(1+x^2)^1/2-1
===================================