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

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

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

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

diverges

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{2} [ln ∣ u ∣]_{a^{2}}^{0}

Compute the boundaries:

diverges

= diverges

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