What is the integral from-1 to-2 of 1/((x-1)^3) ?

The integral from-1 to-2 of 1/((x-1)^3) is 5/72

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integral from-1 to-2 of 1/((x-1)^3)

\int_{- 1}^{- 2} \frac{1}{( x - 1 ) ^{3}} d x

\frac{5}{72}

Decimal

0.06944 \dots

Solution steps

\int_{- 1}^{- 2} \frac{1}{( x - 1 ) ^{3}} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2}^{- 1} \frac{1}{( x - 1 ) ^{3}} d x

Apply u-substitution

: \int_{- 3}^{- 2} \frac{1}{u ^{3}} d u

= - \int_{- 3}^{- 2} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{- 3}^{- 2}

= - [- \frac{1}{2 u ^{2}}]_{- 3}^{- 2}

Compute the boundaries:

- \frac{5}{72}

= - (- \frac{5}{72})

Simplify

= \frac{5}{72}

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What is the integral from-1 to-2 of 1/((x-1)^3) ?
The integral from-1 to-2 of 1/((x-1)^3) is 5/72