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shaqadry

  • 3 years ago

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

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  1. sami-21
    • 3 years ago
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    try substitution t=x^2 dt=2xdx 1/2dt=xdx

  2. shaqadry
    • 3 years ago
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    can i do partial fraction method?

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

  4. sami-21
    • 3 years ago
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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 .

  5. sami-21
    • 3 years ago
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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

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

  7. shaqadry
    • 3 years ago
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    @sami-21 i dont understand

  8. mathsmind
    • 3 years ago
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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...

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

  10. shaqadry
    • 3 years ago
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    okay thank you!

  11. mathsmind
    • 3 years ago
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    you're welcome

  12. mathsmind
    • 3 years ago
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    did u solve the problem?

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