Question

Please help my math
Complete the table

Answer 1

Answer: Check out the attached screenshot to see how the boxes are filled out.

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Work Shown:

`\displaystyle \int \sqrt[7]{x} dx = \int x^(1/7)dx\\\\\\ \displaystyle \int \sqrt[7]{x} dx = (1)/(1+1/7)x^(1+1/7)+C\\\\\\ \displaystyle \int \sqrt[7]{x} dx = (1)/(8/7)x^(8/7)+C\\\\\\ \displaystyle \int \sqrt[7]{x} dx = (7)/(8)x^(8/7)+C\\\\\\`

The rule I used in step 2 is

`\displaystyle \int x^n dx = (1)/(n+1)x^(n +1)+C\\\\\\`

It's basically the same as saying

`\displaystyle \int x^n dx = (x^(n+1))/(n+1)+C\\\\\\`

where
`n \\e -1`. If n = -1, then
`\int x^(-1)dx = \int (1)/(x)dx = \ln(x)+C`