Solving Tricky Integrals: What Technique to Use?

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Homework Statement


Which technique i should use to solve these integrals?


Homework Equations





The Attempt at a Solution


 

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asdnator said:

Homework Statement


Which technique i should use to solve these integrals?


Homework Equations





The Attempt at a Solution

Use the Feynman technique:
  1. Write down the problem.
  2. Think really hard.
  3. Write down the solution.
 
For #5, there's an obvious substitution to try.

For the remaining two, look in your notes and book for techniques to try and take a stab at them. You have to show a reasonable attempt before you can get help here.
 
Is it right?
 

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asdnator said:
Is it right?
You can check it yourself. Take the derivative of your answer. If it's correct, you should end up with the integrand. This is something you should make a habit of doing.
 
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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