I have been trying to find an integral that wolfapha would not compute an answer and I have finaly found out.
My problem I don't know how to solve it.
$$\int \frac{\mathrm{d}x}{x+\sqrt{-x^2}}$$
Some help would be greatly liked.
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$\begingroup$The most sensible interpretation of the problem I can find is to take $\sqrt {-x^2}$ as $\sqrt {(-x)^2}=|x|$ though I think the usual interpretation applies the $-$ after the square and would get $\sqrt{-(x^2)}$ and claim the square root is invalid. Accepting the first, you have $\int \frac {dx}{2x}$ which you can probably solve easily.
$\endgroup$ 5 $\begingroup$I would interpret the integral as either $\int \frac{1}{(1+i\, \text{sgn}\,x)} \frac{dx}{x}$, or invalid as in Ross' answer.
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