`int (8x^3 - 9x^2 + 4) dx` Find the indefinite integral.

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Chapter 4, 4.1 - Problem 14 - 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 (8x^3 - 9x^2 + 4) dx = int 8x^3 dx - int 9x^2 dx + int 4dx`

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

`int 8x^3 dx = (8x^(3+1))/(3 +1) + c => int 8x^3 dx = (8x^4)/(4) + c => int 8x^3 dx = (2x^4) + c`

`int 9x^2 dx = (9x^3)/3 + c => int 9x^2 dx = (3x^3) + c`

`int 4dx = 4x + c`

Gathering the results yields:

`int (8x^3 - 9x^2 + 4) dx = 2x^4 - 3x^3 + c`

Hence, evaluating the indefinite integral, yields` int (8x^3 - 9x^2 + 4) dx = 2x^4 - 3x^3 + 4x + c.`

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