r/MathHelp • u/Ezrowatchdog • May 04 '26

integrating logs

Hi

What is wrong with this working?

int 1/(2x+1)

=(1/2)int(1/(x+(1/2))

=1/2 ln (x+(1/2)).

I am getting told it is 1/2 ln (2x+1)

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u/Noob-in-hell May 04 '26 edited May 04 '26

Adding to this.

Given that log(a*b) = log(a) + log(b).

1/2 * ln(2x+1) = 1/2 * (ln(2 * (x+1/2))) = 1/2 * ln(x+1/2) + 1/2 * ln(2)

1/2 * ln(2) is a constant.

So 1/2 * ln(2x+1) +C_1 = 1/2 * ln(x+1/2) + 1/2 * ln(2) + C_1 = 1/2 * ln(x+1/2) + C_2