Derivatives and Integrals

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Here is a different example that underlines your issue. Both $\frac{x}{x+1}$ and $1-\frac{1}{x+1}$ are exactly the same. The second term is obtained from the first through long division. They both have the same derivative (!) So when the derivative is given as the function to integrate...you found one way and the software found the way. The difference is in the C