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Suppose that we want to compute the following indefinite integral:

The correct solution by Mathematica:

Now here is the (apparently) incorrect solution by using polar coordinates:

[tex]\iint\frac{1}{\sqrt{x^2+y^2}}dxdy=\iint\frac{1}{r}rdrd\theta=(r+c_1)(\theta+c_2)[/tex]

If c_{1}=c_{2}=0, then one solution is:

[tex]r\theta=\sqrt{x^2+y^2}\tan^{-1}\left ( \frac{y}{x} \right )[/tex]

But it isn't:

What's wrong with this solution?

Thanks in advance.

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# A double integral

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