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

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

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integral from 0 to a of 1/((a-x))

\int_{0}^{a} \frac{1}{( a - x )} d x

diverges

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - [ln ∣ u ∣]_{a}^{0}

Compute the boundaries:

diverges

= diverges

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