HELP, how do i integrate (x)^1/3

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To integrate (x)^(1/3) x^(-2/3) / 3, the correct approach involves recognizing the integration formula for x^α, which is ∫x^α dx = (x^(α + 1))/(α + 1) + C, applicable for α ≠ -1. The integration simplifies to (3x^(4/3))/4 after applying the formula correctly. The discussion emphasizes the need to focus on integration rather than differentiation. Ultimately, the final result of the integration process is clarified as (3x^(4/3))/4.
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HELP, URGENT! how do i integrate (x)^1/3

how do i solve this?
please help me integrate (X)^1/3
 
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x^(-2/3) / 3

aka..
1 over 3x^(2/3)
 
The same way you would integrate X^1.

If I were to write X^1 as X^(3/3), would this help you see the similarity? How would you integrate X^(3/3)?
 
okevino said:
x^(-2/3) / 3

aka..
1 over 3x^(2/3)
Errr, well, it's integration, not differentiation. :rolleyes:

For all \alpha \in \mathbb{R}, not -1. We have:
\int x ^ {\alpha} dx = \frac{x ^ {\alpha + 1}}{\alpha + 1} + C

:)
 
opps..
then it's

3x^(4/3) over 4
 

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