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Can some help me do this C4 integration question please (Will rep) :) watch

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    Trying to integrate (e^(2x))/((e^(2x)+1)^3). Its part of the 'using standard patterns to integrate' way of integrating but i just can't understand how it works. The answer is -1/4(e^(2x))/((e^(2x)+1)^2). Thanks
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    Using U-Substitution I get a different answer:

    You should be getting:

    -1/4(e^2x + 1)^-2

    Because:

    Integral = e^2x . 1/u^3 where u = e^2x + 1
    du = 2e^2x dx

    there fore = 1/u^3 . du/2 and take out the factions
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    (Original post by mattismad)
    Using U-Substitution I get a different answer:

    You should be getting:

    -1/4(e^2x + 1)^-2

    Because:

    Integral = e^2x . 1/u^3 where u = e^2x + 1
    du = 2e^2x dx

    there fore = 1/u^3 . du/2 and take out the factions
    sorry, yeah thats the right answer, can you explain the last part sorry i didn't follow
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    (Original post by harry734)
    sorry, yeah thats the right answer, can you explain the last part sorry i didn't follow
    You want to always split things up when working with U-Substitution.

    Then you want to replace what you have with u's

    so earlier we said lets make u=e^2x + 1
    we then want to differentiate it so du/dx= 2e^2x
    we want to replace dx for du so take dx over
    du = 2e^2x dx.

    Earlier we said the integral = e^2x (times by) 1/(e^2x + 1) dx
    Notice, by splitting we can get that e^2x dx.
    If we divide du by 2 it equals = e^2x dx
    This is what we want, so swap our x's for u's
    and bam, then integrate it!
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    (Original post by mattismad)
    You want to always split things up when working with U-Substitution.

    Then you want to replace what you have with u's

    so earlier we said lets make u=e^2x + 1
    we then want to differentiate it so du/dx= 2e^2x
    we want to replace dx for du so take dx over
    du = 2e^2x dx.

    Earlier we said the integral = e^2x (times by) 1/(e^2x + 1) dx
    Notice, by splitting we can get that e^2x dx.
    If we divide du by 2 it equals = e^2x dx
    This is what we want, so swap our x's for u's
    and bam, then integrate it!
    thanks so much, can you integrate this as well? integrate (cos(x))/((cos(x)^2)^(3/2))
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    (Original post by harry734)
    thanks so much, can you integrate this as well? integrate (cos(x))/((cos(x)^2)^(3/2))
    as in? :

    Cos^2(x) or cos(x^2) on the denominator?
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    (Original post by mattismad)
    as in? :

    Cos^2(x) or cos(x^2) on the denominator?
    It's okay i managed to do it eventually haha thanks anyway
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    (Original post by harry734)
    It's okay i managed to do it eventually haha thanks anyway
    No problem mate! Just message me if you have any more questions and I'll see if I can help you!
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    (Original post by mattismad)
    No problem mate! Just message me if you have any more questions and I'll see if I can help you!
    cheers
 
 
 
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