What is the integral from-3 to 2 of (x^3-1)/(x-1) ?

The integral from-3 to 2 of (x^3-1)/(x-1) is 85/6

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integral from-3 to 2 of (x^3-1)/(x-1)

\int_{- 3}^{2} \frac{x ^{3} - 1}{x - 1} d x

\frac{85}{6}

Solution steps

\int_{- 3}^{2} \frac{x ^{3} - 1}{x - 1} d x

Find undefined (singularity) points:

x = 1

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

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

\int_{- 3}^{1} \frac{x ^{3} - 1}{x - 1} d x = \frac{28}{3}

\int_{1}^{2} \frac{x ^{3} - 1}{x - 1} d x = \frac{29}{6}

= \frac{28}{3} + \frac{29}{6}

Simplify

\frac{28}{3} + \frac{29}{6} : \frac{85}{6}

= \frac{85}{6}

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What is the integral from-3 to 2 of (x^3-1)/(x-1) ?
The integral from-3 to 2 of (x^3-1)/(x-1) is 85/6