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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: 12,155 Thanks: 462 Math Focus: Calculus/ODEs  Re: a new discovery in integral calculus??for integral pros
The two results are equivalent, since Now, since is just a constant, this can be added to the constant of integration, and you still have an arbitrary constant added to . 
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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