`int (root(4)(x^3) + 1) dx` Find the indefinite integral.

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Chapter 4, 4.1 - Problem 18 - 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 evaluate the indefinite integral, such that:

`int (root(4)(x^3) + 1) dx = int root(4)(x^3) dx + int dx`

You may use the following formula `int x^n dx = (x^(n+1))/(n+1) + c`

`int root(4)(x^3) dx = int x^(3/4) dx = (x^(3/4+1))/(3/4+1) + c`

`int x^(3/4) dx = (4/7)*(x^(7/4)) + c`

Gathering all the results yields:

`int (root(4)(x^3) + 1) dx = (4/7)*(x^(7/4)) + x + c`

Hence, evaluating the indefinite integral, yields `int (root(4)(x^3) + 1) dx = (4/7)*(x^(7/4)) + x + c.`

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