Integration by Parts to find integral

cummings15
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Homework Statement



find the integral of cot^(-1)of (5x)


Homework Equations



Integration by parts

The Attempt at a Solution



u = x
du = dx
dv = cot ^ (-1)
v = ?

and then i would plug into equation [uv- integral of vdu ]
 
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∫cot-1(5x)dx

It would be more benefical to have u=cot-1(5x) and dv=dx.
 
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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