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July 31st, 2013, 09:13 PM   #1
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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?
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July 31st, 2013, 09:33 PM   #2
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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 .
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July 31st, 2013, 09:54 PM   #3
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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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