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

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

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

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

diverges

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: [- \frac{1}{u}]_{a}^{0}

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

Compute the boundaries:

diverges

= diverges

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