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$7.[-/2$ Points$]$

Consider the following.

${\displaystyle \underset{1}{\overset{4}{}}}\frac{8x^2}{\sqrt[\phantom{2}]{x}}dx$

Use algebra to rewrite the integrand using rational exponents.

${\displaystyle \underset{1}{\overset{4}{}}}\frac{8x^2}{\sqrt[\phantom{2}]{x}}dx={\displaystyle \underset{1}{\overset{4}{}}}(8x^{\frac{1}{2}}{x}^{-\frac{1}{2}})dx$

${\displaystyle \underset{1}{\overset{4}{}}}\frac{8x^2}{\sqrt[\phantom{2}]{x}}dx={\displaystyle \underset{1}{\overset{4}{}}}(8x^{\frac{3}{2}}{x}^{\frac{5}{2}})dx$

${\displaystyle \underset{1}{\overset{4}{}}}\frac{8x^2}{\sqrt[\phantom{2}]{x}}dx={\displaystyle \underset{1}{\overset{4}{}}}(8x^{\frac{1}{2}}{x}^{\frac{3}{2}})dx$

${\displaystyle \underset{1}{\overset{4}{}}}\frac{8x^2}{\sqrt[\phantom{2}]{x}}dx={\displaystyle \underset{1}{\overset{4}{}}}(8x^{-\frac{1}{2}}{x}^{\frac{3}{2}})dx$

${\displaystyle \underset{1}{\overset{4}{}}}\frac{8x^2}{\sqrt[\phantom{2}]{x}}dx={\displaystyle \underset{1}{\overset{4}{}}}(8x^{\frac{1}{2}}{x}^{\frac{5}{2}})dx$

Evaluate the integral.

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