What is the integral from 0 to 1 of (x^7)/(x^8-1) ?

The integral from 0 to 1 of (x^7)/(x^8-1) is diverges

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integral from 0 to 1 of (x^7)/(x^8-1)

\int_{0}^{1} \frac{x ^{7}}{x ^{8} - 1} d x

diverges

Solution steps

\int_{0}^{1} \frac{x ^{7}}{x ^{8} - 1} d x

Apply u-substitution

: \int_{- 1}^{0} \frac{1}{8 u} d u

= \int_{- 1}^{0} \frac{1}{8 u} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int_{- 1}^{0} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{8} [ln ∣ u ∣]_{- 1}^{0}

Compute the boundaries:

diverges

= diverges

\frac{d}{d x} (\frac{x + 2}{x ^{2}})

tan (x), \frac{π}{4}

y^{^{'}} = \frac{2 - e ^{x}}{3 + 2 y}, y (0) = 0

y = \frac{1}{x + k e ^{x}}

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What is the integral from 0 to 1 of (x^7)/(x^8-1) ?
The integral from 0 to 1 of (x^7)/(x^8-1) is diverges