Solving Indefinite Integral: Approach and Techniques

nissan4l0
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Homework Statement


Solve the indefinite integral


Homework Equations


\int\frac{dy}{y(1-y)}

How do I best approach this problem? I have been stuck for hours!
 
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Use partial fractions. That is write 1/(y(1-y)) as:

<br /> \frac{a}{y}+\frac{b}{1-y}

and determine the constants a and b.
 
Ok, thank you! I am taking a differential equations class but I have forgotten about the method of partial fractions. I will relearn it, and I will post my solution shortly.
 
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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