I must be an idiot for seemingly breaking Calculus...

plsmocke

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Sep 8, 2023
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The original question is asking me to integrate the following formula: (4/(x+3)). Simple enough, but I am getting a different result when I bring the 4 down to the denominator before integrating. This form with the 4 in the denominator is (1/(0.25x+0.75)). I was taught that the general rule is the integral of (1/(ax+b))= (1/a)ln|ax+b|dx. What am I doing wrong because even the integrating calculator on this website is giving different results for what I think are the exact same formula:
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4ln(x+34)+C1=4[ln(x+3)ln(4)]+C1=4ln(x+3)4ln(4)+C1another constant=4ln(x+3)+C24\ln\left(\dfrac{x+3}{4}\right) + C_1 = 4[\ln\left(x+3\right)-\ln(4)] +C_1 = 4\ln\left(x+3\right)-\underbrace{ 4\ln(4) +C_1}_{\text{another constant}}= 4\ln\left(x+3\right) + C_2
 
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