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Let's subtract and add 1 to the numerator
= ∫ {( x² - 1) + 1} / ( x - 1 ) dx
= ∫ {( x + 1) • ( x - 1) / ( x - 1)} + {1 / ( x - 1)} dx
= ∫ { ( x + 1) + 1/ ( x - 1) } dx
= ∫ x dx + ∫1• dx + ∫1/( x - 1) dx
= x²/2 + x + ln | x - 1 | + C
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