`int (x^(3/2) + 2x + 1) dx` Find the indefinite integral.

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Chapter 4, 4.1 - Problem 15 - 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^(3/2) + 2x + 1) dx = int x^(3/2) dx + int 2x dx + int dx`

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

`intx^(3/2) dx = (x^(3/2+1))/(3/2 +1) + c => intx^(3/2) dx = (2/5)(x^(5/2)) + c`

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

`int dx = x + c`

Gathering the results yields:

`int (x^(3/2) + 2x + 1) dx = (2/5)(x^(5/2)) + x^2 + x + c`

Hence, evaluating the indefinite integral, yields `int (x^(3/2) + 2x + 1) dx = (2/5)(x^(5/2)) + x^2 + x + c.`

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