Integrate e^(x^1/3): Math Final Help

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Homework Help Overview

The discussion revolves around the integration of the function e^(x^(1/3)), which is part of a math final preparation. The subject area is calculus, specifically focusing on integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks assistance with the integration process. One participant suggests a substitution method, letting x^(1/3) equal t, and provides the differential dx in terms of dt. There is a question regarding the transition from one form of dx to another, indicating a need for clarification on the substitution steps.

Discussion Status

The conversation is ongoing, with participants exploring the substitution method and clarifying the steps involved. Some guidance has been offered regarding the substitution, but there is no explicit consensus on the next steps or the overall approach.

Contextual Notes

The original poster is preparing for a math final, indicating a time constraint and a focus on understanding the integration process without complete solutions being provided.

Playwithmeee
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I have a math final tommorow help please!

How do I integrate e^(x^1/3)

Thank you !
 
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Please show your working .

Just to get you started,
Let x^1/3 = t .
dx = 3x^(2/3)dt = 3t^2dt

Can you go from here ?
 
How did you go from dx = 3x^(2/3)dt to 3t^2dt

Ok I think I get what to do next, substiture dx into the orignal equation?
 
Last edited:
[tex]dx = 3x^{\frac{2}{3}} dt=3\left( x^{\frac{1}{3}}\right) ^{2} = 3t^2dt[/tex]
 

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