anonymous
  • anonymous
integrate 2 / x(x^2+1)^2
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
try substitution t=x^2 dt=2xdx 1/2dt=xdx
anonymous
  • anonymous
can i do partial fraction method?
agent0smith
  • agent0smith
\[\int\limits \frac{ 2 }{ x (x^2+1)^2} dx\] Hmm. Use partial fractions?

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anonymous
  • anonymous
yes you can use partial fraction . i guess fractions will be easy with linear terms so use t=x^2 dt=2xdx \[\Large \int\limits \frac{dt}{t(t+1)^2}\] now use partial fractions .
anonymous
  • anonymous
no we can write the original integral as \[\Large \int\limits \frac{2xdx}{x^2(x^2+1)}\] so let t=x^2 dt=2xdx
anonymous
  • anonymous
\[2\left( \frac{ 1 }{ 2(x^2+1) }-\frac{ 1 }{ 2 }\log(x^2+1)+\log x \right)\]
anonymous
  • anonymous
@sami-21 i dont understand
anonymous
  • anonymous
you can use partial fraction, this is because if the power of the denominator is greater than the power of the numerator that would be an alternative method...
anonymous
  • anonymous
but for me personal i prefer the first method present by sami....
anonymous
  • anonymous
okay thank you!
anonymous
  • anonymous
you're welcome
anonymous
  • anonymous
did u solve the problem?

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