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

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

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

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

\frac{3}{2 ^{\frac{1}{3}}}

Decimal

2.38110 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{2} \frac{1}{u ^{\frac{1}{3}}} d u

= \int_{0}^{2} \frac{1}{u ^{\frac{1}{3}}} d u

Apply the Power Rule

: [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{2}

= [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{2}

Compute the boundaries:

\frac{3}{2 ^{\frac{1}{3}}}

= \frac{3}{2 ^{\frac{1}{3}}}

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