`int (root(3)(x^2)) dx` Find the indefinite integral.

Textbook Question

Chapter 4, 4.1 - Problem 17 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to find the indefinite integral, hence you need to use the following formula:

`int x^n dx = (x^(n+1))/(n+1) + c` 

Replacing `2/3` for n yields:

`int x^(2/3) dx = (x^(2/3+1))/(2/3+1) + c`

`int x^(2/3) dx = (3/5)*x^(5/3) + c`

Hence, evaluating the indefinite integral, yields` int root(3)(x^2) dx = (3/5)*x^(5/3) + c`

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