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Math Help - Integration... Ruins my life...

  1. #1
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    Integration... Ruins my life...

    I missed a week of lectures cuz I messed up my shoulder now I'm struggling to do my assignment...

    <br />
\int \frac{e^{4 x}}{e^{8 x} + 36} dx<br />

    Can anyone please explain how to do that in details?
    I figure you use substitution but it doesn't work out and I cant find another example similar to that in my text or posted notes.
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  2. #2
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    Quote Originally Posted by Lolcats View Post
    <br />
\int \frac{e^{4 x}}{e^{8 x} + 36} dx<br />
    This is clasic \arctan(u) form.
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  3. #3
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    Open the spoiler, if and only if you need more help.

    Spoiler:
    e^{8x}=\left( e^{4x} \right)^{2}, and substitute 6t=e^{4x}.
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  4. #4
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    See thats the thing, I dont know what a classic arctan thing is? I've missed my entire week of lectures so I'm pretty much in the dark to how to do it. Arctan i know the formula and I can follow the steps but I don't know the basis behind it. As to (e^4x)^2 I've realized that but why replace it with 6t? Why not just replace it with u then use du=dx?

    Sorry I know its a struggle to explain a concept over a forum, I just dont have many other resources, just I spent 2 hours at a tutorial in which the TA decided to spend over an hour on one person, being totally oblivious to the other people in the room with questions.
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  5. #5
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    Find the derivative of \frac{1}<br />
{{24}}\arctan \left( {\frac{{e^{4x} }}<br />
{6}} \right)
    What do you see?

    If you cannot do this derivative then this problem is not for you.
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  6. #6
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    uhmmm k I get

    (e^(4x))/(1+((e^(8x))/36)36...

    I don't see how that gets me any closer, regardless if I couldn't do that I wouldn't have much of a choice cuz its on my assignment...
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  7. #7
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    k this is what im getting...
    <br />
\int \displaystyle{\frac{u}{u^{2}+36}\frac{du}{4e^{4x}}  }<br />
    ..then im stuck

    u=e^(4x) and du=4e^(4x)
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  8. #8
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    Quote Originally Posted by Lolcats View Post
    k this is what im getting...
    <br />
\int \displaystyle{\frac{u}{u^{2}+36}\frac{du}{4e^{4x}}  }<br />
    ..then im stuck

    u=e^(4x) and du=4e^(4x)
    Replace that e^{4x} in the denominator with u!
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