`int (x^5 + 1) dx` Find the indefinite integral.

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Chapter 4, 4.1 - Problem 13 - 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, hence, you need to split the integral, such that:

`int (x^5 + 1) dx = int x^5 dx + int dx`

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

Replacing 5 for n yields:

`int x^5 dx = (x^(5+1))/(5 +1) + c`

`int x^5 dx = (x^6)/6 + c`

`int (x^5 + 1) dx = (x^6)/6 + x + c`

Hence, evaluating the indefinite integral, yields `int (x^5 + 1) dx = (x^6)/6 + x + c.`

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