What is the integral from 1 to 3 of (x^2)/(x^3-27) ?

The integral from 1 to 3 of (x^2)/(x^3-27) is diverges

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integral from 1 to 3 of (x^2)/(x^3-27)

\int_{1}^{3} \frac{x ^{2}}{x ^{3} - 27} d x

diverges

Solution steps

\int_{1}^{3} \frac{x ^{2}}{x ^{3} - 27} d x

Apply u-substitution

: \int_{- 26}^{0} \frac{1}{3 u} d u

= \int_{- 26}^{0} \frac{1}{3 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{- 26}^{0} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{- 26}^{0}

Compute the boundaries:

diverges

= diverges

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What is the integral from 1 to 3 of (x^2)/(x^3-27) ?
The integral from 1 to 3 of (x^2)/(x^3-27) is diverges