`int (3/x^7) dx` Find the indefinite integral.

Textbook Question

Chapter 4, 4.1 - Problem 20 - 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 7 for n yields:

`int 3/(x^7) dx = (3x^(-7+1))/(1-7)`

`int 3/(x^7) dx =(3x^(-6))/(-6)`

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

`int 3/(x^7) dx =1/(-2x^6)`

Hence, evaluating the indefinite integral, yields `int 3/(x^7) dx =1/(-2x^6).`

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