anonymous
  • anonymous
int(x/(4+2*x^2) dx what is the answer? (1/4)*ln(2+x^2) or 1/4 *ln(4+2x^2) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Zarkon
  • Zarkon
both ( if you add your constant)
anonymous
  • anonymous
on text the second is the answer whereas on maple the second is answer can you please explain it ?
anonymous
  • anonymous
@Zarkon

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anonymous
  • anonymous
according to the logic the second should be the answer, also when I tried int x/(2*x^2+7*a^2) dx on maple this was the answer (1/4)*ln(2*x^2+7*a^2)
Zarkon
  • Zarkon
that is because they are both correct ... \[\frac{1}{4} \ln(4+2x^2)=\frac{1}{4} \ln(2(2+x^2))=\frac{1}{4} \ln(2)+\frac{1}{4} \ln(2+x^2)\] thus the two answers differ by only a constant
anonymous
  • anonymous
so this difference is trivial?
anonymous
  • anonymous
i mean that can we ignore it? but why?
Zarkon
  • Zarkon
\[\int\frac{x}{4+2x^2}dx\] \[=\frac{1}{4} \ln(4+2x^2)+c_1\] or \[=\frac{1}{4} \ln(2+x^2)+c_2\]
anonymous
  • anonymous
are both answers same?
Zarkon
  • Zarkon
yes...once you include the constant of integration
anonymous
  • anonymous
if I am not wrong have you abosorbed ln(2) in c2?
Zarkon
  • Zarkon
\[\frac{1}{4}\ln(2)\]
anonymous
  • anonymous
yeah
anonymous
  • anonymous
got ittttttttttt
anonymous
  • anonymous
thanks a tonne
Zarkon
  • Zarkon
yw

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