What is the integral from-5 to 5 of 1/(|x|^{2/3)} ?

The integral from-5 to 5 of 1/(|x|^{2/3)} is 6*5^{1/3}

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integral from-5 to 5 of 1/(|x|^{2/3)}

\int_{- 5}^{5} \frac{1}{∣ x ∣ ^{\frac{2}{3}}} d x

6 \cdot 5^{\frac{1}{3}}

Decimal

10.25985 \dots

Solution steps

\int_{- 5}^{5} \frac{1}{∣ x ∣ ^{\frac{2}{3}}} d x

Eliminate Absolutes

= \int_{- 5}^{0} \frac{1}{( - x ) ^{\frac{2}{3}}} d x + \int_{0}^{5} \frac{1}{x ^{\frac{2}{3}}} d x

\int_{- 5}^{0} \frac{1}{( - x ) ^{\frac{2}{3}}} d x = - 3 (- 1)^{\frac{1}{3}} \cdot 5^{\frac{1}{3}}

\int_{0}^{5} \frac{1}{x ^{\frac{2}{3}}} d x = 3 \cdot 5^{\frac{1}{3}}

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

Simplify

- 3 (- 1)^{\frac{1}{3}} \cdot 5^{\frac{1}{3}} + 3 \cdot 5^{\frac{1}{3}} : 6 \cdot 5^{\frac{1}{3}}

= 6 \cdot 5^{\frac{1}{3}}

What is the integral from-5 to 5 of 1/(|x|^{2/3)} ?
The integral from-5 to 5 of 1/(|x|^{2/3)} is 6*5^{1/3}