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MarcLeclair

How can you solve the following integrals:

  • one year ago
  • one year ago

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  1. MarcLeclair
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    \[\int\limits_{a}^{b} e ^{2x}/(1+e^{x}) dx\] --> its just an indefinite integral

    • one year ago
  2. MarcLeclair
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    \[\int\limits_{0}^{1} xln \left| 1 + x ^{2} \right|\]

    • one year ago
  3. MarcLeclair
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    *dx

    • one year ago
  4. hartnn
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    u=1+e^x du = e^x dx e^{2x} = e^x *e^x where e^x = u-1

    • one year ago
  5. MarcLeclair
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    yea im stuck at u-1/ u du

    • one year ago
  6. hartnn
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    for 2nd, 1+x^2=u

    • one year ago
  7. hartnn
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    (u-1)/u = u -1/u

    • one year ago
  8. MarcLeclair
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    oh so i can integrate u/u - 1/u x.x

    • one year ago
  9. MarcLeclair
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    Sorry the x.x isn't part of it

    • one year ago
  10. hartnn
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    yes, you can, easily.

    • one year ago
  11. hartnn
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    for 2nd, you'll just need to integrate ln u

    • one year ago
  12. MarcLeclair
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    I thought I needed to use integration by part for expressions that had the product rule :/

    • one year ago
  13. hartnn
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    when you can substitute and simplify, why go for parts ? :)

    • one year ago
  14. MarcLeclair
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    oooohh and u= 1+ x^2 and du= 2xdx and du/2 = xdx. that was helpful :D

    • one year ago
  15. MarcLeclair
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    so you don't always have to use integration by part when using something that includes the product rule? ( I'm referring to things like xe^x

    • one year ago
  16. hartnn
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    still you'll need integration by parts to integrate ln u

    • one year ago
  17. hartnn
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    not necessary always, forst try substitution

    • one year ago
  18. hartnn
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    *first

    • one year ago
  19. MarcLeclair
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    ah so I have to change the limits of integration then go the integration by part. ALright thanks a lot!!

    • one year ago
  20. hartnn
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    thats correct :) welcome ^_^

    • one year ago
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