Find the integral of: 1 /( cos(u)^(2) sin(u) )

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Homework Statement



Find the integral of:

1 /( cos(u)^(2) sin(u) )

Homework Equations



The problem says to make the 1 in the numerator= sin(u)^(2)+cos(u)^(2)

The Attempt at a Solution



sin(u)^(2)+cos(u)^(2) / ( cos(u)^(2) sin(u) )

(What should I do first?)
 
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Split it up into the addition of 2 fractions, then cancel like products. This will result in 2 fairly simple integrals.
 


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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