Mastering Integration by Parts for Complex Functions

  • Thread starter kesun
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In summary, the conversation is about finding the integral of e to the power of the cube root of x. There are suggestions of using integration by parts and taking the natural logarithm, but it is eventually determined that the integral cannot be expressed in terms of elementary functions. An alternative approach is suggested, using the substitution u^3=x and applying integration by parts twice to solve the integral.
  • #1
kesun
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[tex]\int e^\sqrt[3]{x}[/tex] dx

Integration by parts, perhaps? But if that's the case, I have no idea which is right value for u and which is the right one for dv... Taking ln on both sides? Uh...hmm...I don't think that's how you work this question out...

Any ideas, guys? :|

Thanks!
 
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  • #2
I'm quite certain that integral in not expressible in terms of elementary functions.
 
  • #3
Yeah it can... Let u^3=x
 
Last edited:
  • #4
Feldoh said:
Yeah it can... Let u^3=x

Ahh my bad then. Sorry.
 
  • #5
Feldoh said:
Yeah it can... Let u^3=x

OH YES. First I did that, then I used integration by parts twice to eliminate the u^2 all the way to du, then ta-daa!

Thanks!
 

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