My Math Forum a new discovery in integral calculus??for integral pros only

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 July 31st, 2013, 09:13 PM #1 Member   Joined: Jun 2013 Posts: 42 Thanks: 0 a new discovery in integral calculus??for integral pros only when i was studying i found out that there are times where you shoudn't put the coefficients before the integral sign.. and i think this is a new found discovery because i haven't heard it from others please observe the equation : ? dx/5(x+2)..... we can write it in the form 1/5 ? dx/(x+2) and now its in the form du/u and we can say that the answer is 1/5ln(x+2) + c ----> ans there is another method in solving the equation ? dx/5(x+2) and this time we wont put the coefficient outside the integral sign but instead we will distribute it.. we can write it as ? dx/(5x +10) then we will multiply dx by 5 and divide 1/5 to compensate. so our equaton will be 1/5 ? (5dx)/(5x+10) it is in the form du/u and our answer will be 1/5 ln(5x+10) +c ----->ans and obviously 1/5ln(x+2) ? 1/5ln(5x+10) and i believe that 1/5ln(5x+10) is the correct answer so comments? suggestions?violent reactions?
 July 31st, 2013, 09:33 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,170 Thanks: 472 Math Focus: Calculus/ODEs Re: a new discovery in integral calculus??for integral pros The two results are equivalent, since $\ln(5x+10)=\ln(5(x+2))=\ln(5)+\ln(x+2)$ Now, since $\ln(5)$ is just a constant, this can be added to the constant of integration, and you still have an arbitrary constant added to $\ln(x+2)$.
 July 31st, 2013, 09:54 PM #3 Member   Joined: Jun 2013 Posts: 42 Thanks: 0 Re: a new discovery in integral calculus??for integral pros lol... now that you mentioned it.... i just realized it... and i was so exited that i have discovered something new.i thought i will make history and make gen_shao's theorem and its all ruined... lol.... oh welll.. thnx for the answer...

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