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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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    @MaoYiyi: I was noting exactly what Ross pointed in a complete way below. ;-)2012-12-20

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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.

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    @copper.hat: that is my approach. I think getting answers in both fields may help OP or others with this question.2012-12-20
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I would interpret the integral as either $\int \frac{1}{(1+i\, \text{sgn}\,x)} \frac{dx}{x}$, or invalid as in Ross' answer.