Mastering Integration by Parts for Complex Functions

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\int e^\sqrt[3]{x} 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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I'm quite certain that integral in not expressible in terms of elementary functions.
 
Yeah it can... Let u^3=x
 
Last edited:
Feldoh said:
Yeah it can... Let u^3=x

Ahh my bad then. Sorry.
 
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!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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