# Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 461: 84

The integral converges and its value is $\frac{3}{2}3^{2/3}$.

#### Work Step by Step

We have $$\int_{2}^{5} (5-x)^{-1/3} dx=-\int_{2}^{5} (5-x)^{-1/3} d((5-x)\\ =-\frac{1}{2/3}(5-x)^{2/3}|_{2}^{5}=-\frac{3}{2}(0-3^{2/3})=\frac{3}{2}3^{2/3}$$ Hence, the integral converges and its value is $\frac{3}{2}3^{2/3}$.

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