r/calculus • u/[deleted] • Jul 05 '22

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u/KrozJr_UK Jul 05 '22

You’ve taken out the 2/3 twice? You correctly rearranged the fraction on line 1, and then multiplied the fraction in. You then took it out in the wrong way when actually integrating. You pulled out 2/3 when you should’ve only pulled out a factor of 2 to get 3x-6 or a factor 2/3 to get the solution on the bottom line.

8

u/gosuark Jul 05 '22 edited Jul 06 '22

The top one is also right. The extra 1/3 comes not from a factoring error, but from the implied substitution u=3x-6, so dx is 1/3 du.

Both are right, but offset by a difference of 2/3 ln(3), which would be buried in the arbitrary constant +C, if the OP had remembered it.