How to Integrate a Fraction with a Square Root in the Denominator

nyyfan0729
12
0
Can somebody tell me step by step how to integrate (x^5)/((1-2x^3)^(1/2)).
 
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Have you tried the substitution y = \sqrt {1 - 2x^3 }?
 
I don't know what you have in mind TD. I would substitute u = 1 - 2x^3, with x^3 = (1 - u)/2
 
They're essentially the same thing. But I tend to prefer TD's because it gets rid of all the messy radicals!

nyyfan0729: we're not here to do the problems for you step by step. (that's already done in your textbook and solution manual anyways) We're here to help you when you're stuck: you need to show us your thoughts on the problem, and what you've tried, so that we know where you're stuck and why.
 

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 . 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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