Trigonometric Substitution Triangles

CpE Maj
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Homework Statement



This may be basic, but how do you know which part of an integration problem fill the up the triangle values for trig substitution?
 
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Welcome to PF!

Hi CpE Maj! Welcome to PF! :wink:
CpE Maj said:
This may be basic, but how do you know which part of an integration problem fill the up the triangle values for trig substitution?

I don't understand. :confused:

Can you give an example? :smile:​
 

Thread 'Finding the nth roots of a complex number'

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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