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Hence f(x) = g(x) + h (x)

where g(x) = x / [ x² - x ]  = 1/(x-1)  and  h(x) = √x / [ x² - x ]  = 1 / [ √x (x-1) ]

Let u = √x

du =  [ 1 / ( 2 √x ) ] dx

Hence  ( dx / √x ) = 2 du

Hence , we rewrite the second integration as

If we write the second integrand function as partial fracion , then we have

Hence above integration becomes

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