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So Wolfram Alpha and Symbolab have different reuslt for this integral $\int \frac{x}{x+2}dx$. I done it myself and got result like Wolfram Alpha : $x-2\ln|x+2|$. Symbolab display this one: $x+2-2\ln|x+2|$. So which one is now more reliable?

Input on Wolfram Alpha and Symbolab

Wolfram solved

Symbolab solved

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2 Answers

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Note that the "$+2$" from Symbolab's solution is a constant, and can be "merged in", so to speak, with the constant of integration "$+C$" (since the sum of two constants is just another constant). Ergo, the two solutions are equivalent (since that's the only meaningful point in which the two differ).

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Both expressions are equivalent that is to say the "$2$" actually gets "absorbed" into the constant term.

$$\begin{aligned}\int\dfrac{x}{x+2}\mathrm dx&=x+2-2\ln\mid x+2\mid+C \\&=x-2\ln\mid x+2\mid +\left(\color{red}{C+2}\right)\\&=x-2\ln\mid x+2\mid +C'\end{aligned}$$

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