نحول التكامل الي الشكل

=int[ x^2/(x^2-4)^(3/2)]dx
x^2-4=t^(1/1.5); t=(x^2-4)^(1.5)
2xdx=1/1.5*t^(-0.5/1.5)dt
J=int [4+t^(1/1.5)]*
* t^(-0.5/1.5)dt]/t^(1/1.5)=
=int [4+t^(1/1.5)]/t*dt=
=4*intdt/t+int t^(-1/3)dt=
=4lnt+3/2*t(^2/3)=
=6ln|x^2-4| +(x^2-4)^(2/3)+c