Question

Integrate (sqrt((x-1)/x^5)) using substitution (no trig substitution) ...?

Answer 1

√ (( x - 1) / x^5) = 1/√x^4 · √(1 - 1/x )= 1/x² · √( 1 - 1/x )
Substitution:
u = 1 - 1/x
d u = 1/x² dx

`\int { (1)/( x^(2) ) * √(1-1/x) } \, dx= \\ = \int { √(u) } \, du= \\ =2/3u √(u)= \\ =2/3(1-1/x) √(1-1/x)+C`