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

The integral from 2 to 3 of 1/((x-1)^3) is 3/8

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

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

\frac{3}{8}

Decimal

0.375

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

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

Compute the boundaries:

\frac{3}{8}

= \frac{3}{8}

What is the integral from 2 to 3 of 1/((x-1)^3) ?
The integral from 2 to 3 of 1/((x-1)^3) is 3/8