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The constant term in the expansion of (x+log_e(1-x))/x³ is

Dear Student,

\frac{x + \log_{e} (1 - x)}{x^{3}} = \frac{x + (- x - \frac{x^{2}}{2} - \frac{x^{3}}{3} - \frac{x^{4}}{4} - . . .)}{x^{3}} = \frac{x - x - \frac{x^{2}}{2} - \frac{x^{3}}{3} - \frac{x^{4}}{4} - . . .}{x^{3}} = \frac{- \frac{x^{2}}{2} - \frac{x^{3}}{3} - \frac{x^{4}}{4} - . . .}{x^{3}} = \frac{1}{x^{3}} (- \frac{x^{2}}{2} - \frac{x^{3}}{3} - \frac{x^{4}}{4} - . . .) = (- \frac{1}{2 x} - \frac{1}{3} - \frac{x}{4} - . . .) H e n c e c o n s \tan t t e r m i s - \frac{1}{3} .

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