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Verified Answer :

HomertheGenius

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

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