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shaqadry

integrate 2 / x(x^2+1)^2

  • one year ago
  • one year ago

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  1. sami-21
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    try substitution t=x^2 dt=2xdx 1/2dt=xdx

    • one year ago
  2. shaqadry
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    can i do partial fraction method?

    • one year ago
  3. agent0smith
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    \[\int\limits \frac{ 2 }{ x (x^2+1)^2} dx\] Hmm. Use partial fractions?

    • one year ago
  4. sami-21
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    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 .

    • one year ago
  5. sami-21
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    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

    • one year ago
  6. deena123
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    \[2\left( \frac{ 1 }{ 2(x^2+1) }-\frac{ 1 }{ 2 }\log(x^2+1)+\log x \right)\]

    • one year ago
  7. shaqadry
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    @sami-21 i dont understand

    • one year ago
  8. mathsmind
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    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...

    • one year ago
  9. mathsmind
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    but for me personal i prefer the first method present by sami....

    • one year ago
  10. shaqadry
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    okay thank you!

    • one year ago
  11. mathsmind
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    you're welcome

    • one year ago
  12. mathsmind
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    did u solve the problem?

    • one year ago
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