Integrate -x3-x2-x-1x-1dx

x^3 x^2+x 1=x^2(x 1)+(x 1)=(x^2+1)(x 1) ⇒ I=∫ (x^2+1)dx=x^33+x+c . ...

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Algebraic Identity (a-b)^3

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Question

Integrate $\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x$

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Solution

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\int \frac{x}{x^{3} + x^{2} + x + 1} d x

Integrate the rational functions.
$\int \frac{x^{3} + x + 1}{x^{2} - 1} d x .$

\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x

Find the following integrals.
$\int \frac{x^{3} - x^{2} + x - 1}{(x - 1)} d x .$

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$\int \frac{3 x + 5}{x^{3} - x^{2} - x + 1} d x .$

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