Answer: Check out the attached screenshot to see how the boxes are filled out.
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Work Shown:
[tex]\displaystyle \int \sqrt[7]{x} dx = \int x^{1/7}dx\\\\\\
\displaystyle \int \sqrt[7]{x} dx = \frac{1}{1+1/7}x^{1+1/7}+C\\\\\\
\displaystyle \int \sqrt[7]{x} dx = \frac{1}{8/7}x^{8/7}+C\\\\\\
\displaystyle \int \sqrt[7]{x} dx = \frac{7}{8}x^{8/7}+C\\\\\\[/tex]
The rule I used in step 2 is
[tex]\displaystyle \int x^n dx = \frac{1}{n+1}x^{n +1}+C\\\\\\[/tex]
It's basically the same as saying
[tex]\displaystyle \int x^n dx = \frac{x^{n+1}}{n+1}+C\\\\\\[/tex]
where [tex]n \ne -1[/tex]. If n = -1, then [tex]\int x^{-1}dx = \int \frac{1}{x}dx = \ln(x)+C[/tex]
