What is the integral of \sqrt[3]{x^2-2x+1} ?

The integral of \sqrt[3]{x^2-2x+1} is 3/5 (x-1)^{5/3}+C

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integral of \sqrt[3]{x^2-2x+1}

\frac{3}{5} (x - 1)^{\frac{5}{3}} + C

Solution steps

Complete the square

x^{2} - 2 x + 1 : (x - 1)^{2}

Apply u-substitution

: \int u^{\frac{2}{3}} d u

= \int u^{\frac{2}{3}} d u

Apply the Power Rule

: \frac{3}{5} u^{\frac{5}{3}}

= \frac{3}{5} u^{\frac{5}{3}}

Substitute back

u = x - 1

= \frac{3}{5} (x - 1)^{\frac{5}{3}}

Add a constant to the solution

= \frac{3}{5} (x - 1)^{\frac{5}{3}} + C

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What is the integral of \sqrt[3]{x^2-2x+1} ?
The integral of \sqrt[3]{x^2-2x+1} is 3/5 (x-1)^{5/3}+C