Evaluate the following integral ∫1/(x^3 (1+x)^4 ) dx

Put   z=(x+1)/x       then     x=1/(1+z)     dx=-dz⁄(z+1)^2
I=-∫(z+1)^5/z^4  dz

(z-1)^5=z^5-5z^4+10z^3-10z^2+5z-1
I=-∫(z^5-5z^4+10z^3-10z^2+5z-1)/z^4  dz
=z^2/2+5z+10 ln⁡z-10/z-5/(2z^2 )-3/z^3 +c
=((x+1)/x)^2/2-5((x+1)/x)+10 ln⁡((x+1)/x)-10/(((x+1)/x) )-5/(2((x+1)/x)^2 )-3/((x+1)/x)^3 +c