Get Expert Help with Integration Homework - Essential Equations & Solutions

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Homework Statement



http://prikachi.com/images/201/4687201t.gif

Homework Equations



Given in class on material connected with undefined integral

The Attempt at a Solution


Hard for me to grasp that one...
P.S Thanks in advance
 
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Use integration by partial fractions.
 
grindfreak said:
Use integration by partial fractions.
The integrand is not a rational expression, so I don't see how this technique could work.

A better approach, I believe, is to complete the square inside the radical, and then use a trig substitution.
 
Hmmm, good point trig substitution would probably work.
 
I finally done it with a little help from a friend :)
http://prikachi.com/images/946/4687946U.gif
which is arcsin√x +C
 
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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