What is the integral from 0 to 1 of x/(x^2-1) ?

The integral from 0 to 1 of x/(x^2-1) is diverges

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integral from 0 to 1 of x/(x^2-1)

\int_{0}^{1} \frac{x}{x ^{2} - 1} d x

diverges

Solution steps

\int_{0}^{1} \frac{x}{x ^{2} - 1} d x

Apply u-substitution

: \int_{- 1}^{0} \frac{1}{2 u} d u

= \int_{- 1}^{0} \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{- 1}^{0} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{- 1}^{0}

Compute the boundaries:

diverges

= diverges

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\int_{0}^{1} (x^{2} - x + 1) d x

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\int_{0}^{1} \frac{e ^{x} + 4}{e ^{x}} d x

What is the integral from 0 to 1 of x/(x^2-1) ?
The integral from 0 to 1 of x/(x^2-1) is diverges