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

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

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

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

- \frac{5}{72}

Decimal

- 0.06944 \dots

Solution steps

\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}

7 x + 12, 0, 10

\frac{1}{s ^{3} ( s + 2 )}

\frac{\partial}{\partial x} (x^{2} y + y^{2} z + z^{2} x)

x^{- 2} y^{- 5} d x + x^{- 3} y^{- 4} d y = 0

\int \frac{x ^{2}}{1 + x ^{3}} d x

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