anonymous
  • anonymous
integral of (3v/(1-4v^2))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Psymon
  • Psymon
Just let u be the denominator for your u-substitution. u = 1-4v^2, so du = -8vdx and dx = -du/8v
anonymous
  • anonymous
\[x(dv/dx)=(1-4v^2/3v) \]
anonymous
  • anonymous
i have to solve the equation

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Psymon
  • Psymon
3v is dividing all of 1-4v^2?
anonymous
  • anonymous
yea
Psymon
  • Psymon
Im guessing it is considering your first question. Then yeah, looked like you had the write idea, separation of variables. So we have: \[\int\limits_{}^{}\frac{ 3v }{ 1-4v ^{2} }dv=\int\limits_{}^{}\frac{ 1 }{ x }dx\]So as I aning mentioned before, you can let u be 1-4v^2. meaning du = -8vdv and dv = -du/8v. The right integral is just an immediate integration into ln. So all of this gives us: \[3\int\limits_{}^{}\frac{ }{ }\frac{ v }{ u }*\frac{ -du }{ 8v }=\int\limits_{}^{}\frac{ 1 }{ u }du\] \[-\frac{ 3 }{ 8 }\ln|1-4v ^{2}|=\ln|x|+C\] Would you know how to take it from there?
anonymous
  • anonymous
yea thanks so much!!!
Psymon
  • Psymon
Yep, np ^_^

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