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Standard Formulae - 1

∫x3-x2+x-1x-1...

Question

$\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x$ is equal to
(where $C$ is constant of integration)

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Solution

$\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x = \int \frac{x^{2} (x - 1) + x - 1}{x - 1} d x = \int (x^{2} + 1) d x$
By taking the terms separately, we get
$= \int x^{2} d x + \int 1 d x$
Therefore, we obtain
$= \frac{x^{3}}{3} + x + C$

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