What is the integral of 1/(u^2)\sqrt[3]{1-1/u} ?

The integral of 1/(u^2)\sqrt[3]{1-1/u} is 3/4 ((u-1)/u)^{4/3}+C

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integral of 1/(u^2)\sqrt[3]{1-1/u}

\frac{3}{4} (\frac{u - 1}{u})^{\frac{4}{3}} + C

Solution steps

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply the Power Rule

: \frac{3}{4} w^{\frac{4}{3}}

= - (- \frac{3}{4} w^{\frac{4}{3}})

Substitute back

= - (- \frac{3}{4} (1 - \frac{1}{u})^{\frac{4}{3}})

Simplify

- (- \frac{3}{4} (1 - \frac{1}{u})^{\frac{4}{3}}) : \frac{3}{4} (\frac{u - 1}{u})^{\frac{4}{3}}

= \frac{3}{4} (\frac{u - 1}{u})^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{4} (\frac{u - 1}{u})^{\frac{4}{3}} + C

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What is the integral of 1/(u^2)\sqrt[3]{1-1/u} ?
The integral of 1/(u^2)\sqrt[3]{1-1/u} is 3/4 ((u-1)/u)^{4/3}+C