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

Textbook Question

Chapter 4, 4.1 - Problem 19 - 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 1/(x^n) dx = (x^(-n+1))/(1-n)`

Replacing 5 for n yields:

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

`int 1/(x^5) dx =(x^(-4))/(-4)`

You need to remember that `x^(-n) = 1/(x^n):`

`int 1/(x^5) dx =1/(-4x^4)`

Hence, evaluating the indefinite integral, yields` int 1/(x^5) dx =1/(-4x^4).`

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