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

  • Thread starter Playwithmeee
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In summary, the formula for integrating e^(x^1/3) is ∫e^(x^1/3)dx = 3x^1/3e^(x^1/3) + C. The process for integrating e^(x^1/3) involves using u-substitution, and there are special rules to keep in mind, such as always including the constant of integration and involving the original function in the final answer. Some common mistakes to avoid include forgetting the constant of integration and making errors in the u-substitution process. An example problem of integrating e^(x^1/3) is ∫e^(x^1/3)dx, which can be solved by using u-substitution and
  • #1
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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  • #2
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 ?
 
  • #3
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?
 
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  • #4
[tex]dx = 3x^{\frac{2}{3}} dt=3\left( x^{\frac{1}{3}}\right) ^{2} = 3t^2dt[/tex]
 

What is the formula for integrating e^(x^1/3)?

The formula for integrating e^(x^1/3) is ∫e^(x^1/3)dx = 3x^1/3e^(x^1/3) + C.

What is the process for integrating e^(x^1/3)?

The process for integrating e^(x^1/3) involves using u-substitution. Let u = x^1/3, then the integral becomes ∫e^u * 3u^2du, which can then be integrated using the power rule.

Are there any special properties or rules to keep in mind when integrating e^(x^1/3)?

Yes, there are a few special rules to keep in mind when integrating e^(x^1/3). One is that the constant of integration (C) is always necessary in the final answer. Another is that the integral of e^(x^1/3) will always involve the original function e^(x^1/3) in some way.

What are some common mistakes to avoid when integrating e^(x^1/3)?

Common mistakes when integrating e^(x^1/3) include forgetting to include the constant of integration, making errors in the u-substitution process, and forgetting to use the power rule when integrating the u-term.

Can you provide an example problem of integrating e^(x^1/3)?

Sure, an example problem of integrating e^(x^1/3) would be ∫e^(x^1/3)dx. Using u-substitution, let u = x^1/3, then the integral becomes ∫e^u * 3u^2du. Using the power rule, we get 3u^3/3 + C = u^3 + C = x + C. So, the final answer is 3x^1/3e^(x^1/3) + C.

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