The discussion focuses on the integration of logarithmic functions, specifically the indefinite integrals of the forms \(\frac{1}{2}\int \frac{dx}{x+1}\) and \(\int \frac{dx}{2x+2}\). Both integrals yield results that differ only by an additive constant, as demonstrated by the equation \(\frac{1}{2}\log(2x+2) = \frac{1}{2}\log(x+1) + \log\sqrt{2}\). This confirms that both expressions are valid representations of the indefinite integrals.
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Mute said:Those are indefinite integrals, so they're only unique up to an additive constant. Notice:
[tex]\frac{1}{2}\log(2x+2) = \frac{1}{2}\log(x+1) + \log\sqrt{2}[/tex]
hence the two integrals differ only by a constant, and both are correct.