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I have just encountered a strange (for me) inconsistency with a derivative: If I take the x derivative of ##\frac{x}{x+a}## I get ##\frac{x+a-x}{(x+a)^2} = \frac{a}{(x+a)^2}##. However, when I take the integral of the latter I get: ##-\frac{a}{x+a} (+constant) ≠ \frac{x}{x+a}##. I have checked the above (simple) calculations with Mathematica to make sure I didn't make any mistake with formulas/arithmetic. Maybe I forget some principle but how is it possible to integrate the derivative of a function and get something else than the function itself back?

Appreciate any help on this.

Just for the record, I have attached a screenshot of Mathematica.

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# A strange derivative-integral discrepancy

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