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MarcLeclair

  • 3 years ago

How can you solve the following integrals:

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

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

  3. MarcLeclair
    • 3 years ago
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    *dx

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

  5. MarcLeclair
    • 3 years ago
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    yea im stuck at u-1/ u du

  6. hartnn
    • 3 years ago
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    for 2nd, 1+x^2=u

  7. hartnn
    • 3 years ago
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    (u-1)/u = u -1/u

  8. MarcLeclair
    • 3 years ago
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    oh so i can integrate u/u - 1/u x.x

  9. MarcLeclair
    • 3 years ago
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    Sorry the x.x isn't part of it

  10. hartnn
    • 3 years ago
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    yes, you can, easily.

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

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

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

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

  15. MarcLeclair
    • 3 years ago
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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

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

  17. hartnn
    • 3 years ago
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    not necessary always, forst try substitution

  18. hartnn
    • 3 years ago
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    *first

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

  20. hartnn
    • 3 years ago
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    thats correct :) welcome ^_^

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