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    (Original post by tigerz)
    LOOL, I don't know why I chose this nickname :dontknow: I was making the account in a hurry :P Although tigers are pretty cool: http://24.media.tumblr.com/tumblr_m6...xc0mo1_500.jpg  \leftarrow bare cute! :h:

    Then again I have a dog called Simba..

    LOLs, how much more exams have you got left? How many of them are maths?
    Isn't Simba a Lion's name. Nice pic link btw.
    I have 4 more exams left. Only 2 of them are maths: C3 and C4. Is my sig not appearing anymore? My exam info should be in it.
    I was meant to be starting exam revision today, unfortunately I seem to have more housework (or should I say flatwork?) to complete. I should be done before it's time to prepare tea so I can do a couple past papers in the evening. It's okay to be relaxed about it I think! As long as I do a healthy amount of past papers per day.
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    (Original post by MathsNerd1)
    I can wait that long


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    (Original post by joostan)
    Quote me in the solution will you?
    Spoiler:
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    I think I may be going out for a spin in a bit
    I ****ing execrate all of you

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    I = \displaystyle\int \dfrac{dx}{(x+q) \sqrt{ax^{2} + bx + c}}

    Let x + q = t^{-1} \Rightarrow I = - \displaystyle\int \dfrac{dt}{\sqrt{t^{2}} \sqrt{ax^{2} + bx + c}}

    = - \displaystyle\int \dfrac{dt}{\sqrt{(aq^{2} - bq + c) t^{2} + (b-2aq)t + a}}

    Let aq^{2} - bq + c = \alpha, b - 2aq = \beta (yes it's cheating, so bite me :teehee: )

    I = - \displaystyle\int \dfrac{dt}{\sqrt{ \alpha t^{2} + \beta t + a}}

    = - \dfrac{1}{\sqrt{ \alpha }}\displaystyle\int \dfrac{dt}{\sqrt{ \left[t + \frac{\beta}{2 \alpha} \right]^{2} + \frac{a}{\alpha} - \frac{\beta^{2}}{4 \alpha^{2}}}}

    Let  \frac{a}{\alpha} - \frac{\beta^{2}}{4 \alpha^{2}} = \gamma (bite me :teehee:)

    Let \left[t + \frac{\beta}{2 \alpha} \right] = \gamma \tan u

    \Rightarrow I = - \dfrac{1}{ \sqrt{\alpha}} \displaystyle\int \sec u du

    = - \dfrac{1}{ \sqrt{\alpha}} \ln (\sec u + \tan u ) + \mathcal{C}

     = - \dfrac{1}{ \sqrt{\alpha}} \ln \left( \sec \left( \dfrac{ [t + \frac{ \beta}{2 \alpha} ]}{\gamma} \right) + \left( \dfrac{ [t + \frac{ \beta}{2 \alpha} ]}{\gamma} \right) \right) + \mathcal{C}

     = - \dfrac{1}{\sqrt{\alpha}} \ln \left( \left( \dfrac{ [t + \frac{\beta}{2 \alpha} ]}{\gamma} \right) + \sqrt{1 + \dfrac{ [ t + \frac{\beta}{2 \alpha} ]^{2}}{\gamma^{2}}} \right)  + \mathcal{C}

    where t = x + q, \alpha = aq^{2} - bq + c, \beta = b - 2aq, \gamma = \dfrac{a}{\alpha} - \dfrac{\beta^{2}}{4 \alpha^{2}}

    Who amongst you are courageous enough to endeavour in the righteous quest of checking my working? :teehee:
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    (Original post by reubenkinara)
    Isn't Simba a Lion's name. Nice pic link btw.
    I have 4 more exams left. Only 2 of them are maths: C3 and C4. Is my sig not appearing anymore? My exam info should be in it.
    I was meant to be starting exam revision today, unfortunately I seem to have more housework (or should I say flatwork?) to complete. I should be done before it's time to prepare tea so I can do a couple past papers in the evening. It's okay to be relaxed about it I think! As long as I do a healthy amount of past papers per day.
    Yup, my dog has a lions name ^_^ Why thank you, when I was little I wanted I baby white tiger but then realised it may be slightly inconvenient!
    :O Never knew about that, looks cool! Ah I've been putting chores of for a while but they are slowly returning, gonna end up being a maid after exams to make up for it, yeah same I feel the same way although i'm only managing to get 1 paper in these days, I need to do at least 2/3 for it to be sufficient revision haha, I think I feel a little too relaxed!
    Good luck with the rest of your exams, you'll be fine! The c3 and c4 papers are reserves let me know how they went
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    (Original post by Felix Felicis)
    I ****ing execrate all of you

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    I = \displaystyle\int \dfrac{dx}{(x+q) \sqrt{ax^{2} + bx + c}}

    Let x + q = t^{-1} \Rightarrow I = - \displaystyle\int \dfrac{dt}{\sqrt{t^{2}} \sqrt{ax^{2} + bx + c}}

    = - \displaystyle\int \dfrac{dt}{\sqrt{(aq^{2} - bq + c) t^{2} + (b-2aq)t + a}}

    Let aq^{2} - bq + c = \alpha, b - 2aq = \beta (yes it's cheating, so bite me :teehee: )

    I = - \displaystyle\int \dfrac{dt}{\sqrt{ \alpha^{2} t^{2} + \beta t + a}}

    = - \dfrac{1}{\sqrt{ \alpha }}\displaystyle\int \dfrac{dt}{\sqrt{ \left[t + \frac{\beta}{2 \alpha} \right]^{2} + \frac{a}{\alpha} - \frac{\beta^{2}}{4 \alpha^{2}}}}

    Let  \frac{a}{\alpha} - \frac{\beta^{2}}{4 \alpha^{2}} = \gamma (bite me :teehee:)

    Let \left[t + \frac{\beta}{2 \alpha} \right] = \gamma \tan u

    \Rightarrow I = - \dfrac{1}{\alpha} \displaystyle\int \sec u du

    = - \dfrac{1}{ \sqrt{\alpha}} \ln (\sec u + \tan u ) + \mathcal{C}

     = - \dfrac{1}{ \sqrt{\alpha}} \ln \left( \sec \left( \dfrac{ [t + \frac{ \beta}{2 \alpha} ]}{\gamma} \right) + \left( \dfrac{ [t + \frac{ \beta}{2 \alpha} ]}{\gamma} \right) \right) + \mathcal{C}

     = - \dfrac{1}{\sqrt{\alpha}} \ln \left( \left( \dfrac{ [t + \frac{\beta}{2 \alpha} ]}{\gamma} \right) + \sqrt{1 + \dfrac{ [ t + \frac{\beta}{2 \alpha} ]^{2}}{\gamma^{2}}} \right)  + \mathcal{C}

    where t = x + q, \alpha = aq^{2} - bq + c, \beta = b - 2aq, \gamma = \dfrac{a}{\alpha} - \dfrac{\beta^{2}}{4 \alpha^{2}}

    Who amongst you are courageous enough to endeavour in the righteous quest of checking my working? :teehee:
    So that is how you dealt with the other quadratic, I never thought to simply make it equal another greek letter, I must say though that looks pretty damn impressive!
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    (Original post by MathsNerd1)
    So that is how you dealt with the other quadratic, I never thought to simply make it equal another greek letter, I must say though that looks pretty damn impressive!
    It's just completing the square - I only let the terms equal to something else so I don't die from the algebra :teehee:
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    (Original post by Felix Felicis)
    I ****ing execrate all of you

    Spoiler:
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    I = \displaystyle\int \dfrac{dx}{(x+q) \sqrt{ax^{2} + bx + c}}

    Let x + q = t^{-1} \rightarrow I = - \displaystyle\int \dfrac{dt}{\sqrt{t^{2}} \sqrt{ax^{2} + bx + c}}

    = - \displaystyle\int \dfrac{dt}{\sqrt{(aq^{2} - bq + c) t^{2} + (b-2aq)t + a}}

    Let aq^{2} - bq + c = \alpha, b - 2aq = \beta (yes it's cheating, so bite me :teehee: )

    I = - \displaystyle\int \dfrac{dt}{\sqrt{ \alpha^{2} t^{2} + \beta t + a}}

    = - \dfrac{1}{\sqrt{ \alpha }}\displaystyle\int \dfrac{dt}{\sqrt{ \left[t + \frac{\beta}{2 \alpha} \right]^{2} + \frac{a}{\alpha} - \frac{\beta^{2}}{4 \alpha^{2}}}}

    Let  \frac{a}{\alpha} - \frac{\beta^{2}}{4 \alpha^{2}} = \gamma (bite me :teehee:)

    Let \left[t + \frac{\beta}{2 \alpha} \right] = \gamma \tan u

    \rightarrow I = - \dfrac{1}{\alpha} \displaystyle\int \sec u du

    = - \dfrac{1}{ \sqrt{\alpha}} \ln (\sec u + \tan u ) + \mathcal{C}

     = - \dfrac{1}{ \sqrt{\alpha}} \ln \left( \sec \left( \dfrac{ [t + \frac{ \beta}{2 \alpha} ]}{\gamma} \right) + \left( \dfrac{ [t + \frac{ \beta}{2 \alpha} ]}{\gamma} \right) \right) + \mathcal{C}

     = - \dfrac{1}{\sqrt{\alpha}} \ln \left( \left( \dfrac{ [t + \frac{\beta}{2 \alpha} ]}{\gamma} \right) + \sqrt{1 + \dfrac{ [ t + \frac{\beta}{2 \alpha} ]^{2}}{\gamma^{2}}} \right)  + \mathcal{C}

    where t = x + q, \alpha = aq^{2} - bq + c, \beta = b - 2aq, \gamma = \dfrac{a}{\alpha} - \dfrac{\beta^{2}}{4 \alpha^{2}}

    Who amongst you are courageous enough to endeavour in the righteous quest of checking my working? :teehee:
    I can't check Looks correct . Felix, when doing this type of stuff do you do it/think whilst typing the latex or do you type the latex after doing it on paper?
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    (Original post by Felix Felicis)
    It's just completing the square - I only let the terms equal to something else so I don't die from the algebra :teehee:
    What doesn't kill you, makes you stronger.
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    (Original post by reubenkinara)
    I can't check Looks correct . Felix, when doing this type of stuff do you do it/think whilst typing the latex or do you type the latex after doing it on paper?
    I do the problem whilst typing it in LaTeX brah :teehee:
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    (Original post by Felix Felicis)
    It's just completing the square - I only let the terms equal to something else so I don't die from the algebra :teehee:
    And there was me trying my best to hack through all the horrendous algebra and you do go and simplify it all, why the hell didn't I think of that! Stupid me :mad:
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    (Original post by Felix Felicis)
    I do the problem whilst typing it in LaTeX brah :teehee:
    Wow :eek:
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    (Original post by MathsNerd1)
    And there was me trying my best to hack through all the horrendous algebra and you do go and simplify it all, why the hell didn't I think of that! Stupid me :mad:
    Well now, you've picked up a neat trick that may prove helpful in the future .
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    (Original post by reubenkinara)
    Well now, you've picked up a neat trick that may prove helpful in the future .
    Indeed, always just simplify whenever I find something that looks horrible and deal with it all at the end
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    (Original post by Felix Felicis)
    I do the problem whilst typing it in LaTeX brah :teehee:
    amazing- 'nuff said

    Can you always just equate to a random sign? and then deal with it later?
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    (Original post by tigerz)
    amazing- 'nuff said

    Can you always just equate to a random sign? and then deal with it later?
    Yeah, it's still the same thing

    EDIT: Can I just point out - if it's a hard problem on which I actually need to think, I do it on paper. :lol: If it's like the integral from that AEA question, then just LaTeX
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    (Original post by Felix Felicis)
    Yeah, it's still the same thing

    EDIT: Can I just point out - if it's a hard problem on which I actually need to think, I do it on paper. :lol: If it's like the integral from that AEA question, then just LaTeX
    awesome, so do alpha, beta and gamma mean anything specific in maths?
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    (Original post by tigerz)
    awesome, so do alpha, beta and gamma mean anything specific in maths?
    They're just greek letters - I'm sure they're used in conventions to mean things specifically (for example, \gamma is commonly used to denote the Lorentz factor in special relativity) but I just used them as they're the first that came to my mind :lol: I could've used a penis as the placeholder if I really wanted to :teehee:
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    (Original post by Felix Felicis)
    They're just greek letters - I'm sure they're used in conventions to mean things specifically (for example, \gamma is commonly used to denote the Lorentz factor in special relativity) but I just used them as they're the first that came to my mind :lol: I could've used a penis as the placeholder if I really wanted to :teehee:
    I love using lambda personally, and will throw it in whenever I get the opportunity.
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    (Original post by DJMayes)
    I love using lambda personally, and will throw it in whenever I get the opportunity.
    Too true! Lambda is one sexy letter :coma: I use a curly w sometimes, don't know why, just do, it looks cool :teehee: Like w
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    (Original post by Felix Felicis)
    Yeah, it's still the same thing

    EDIT: Can I just point out - if it's a hard problem on which I actually need to think, I do it on paper. :lol: If it's like the integral from that AEA question, then just LaTeX
    Haha, and you finding a problem hard is a difficult task in itself

    (Original post by Felix Felicis)
    They're just greek letters - I'm sure they're used in conventions to mean things specifically (for example, \gamma is commonly used to denote the Lorentz factor in special relativity) but I just used them as they're the first that came to my mind :lol: I could've used a penis as the placeholder if I really wanted to :teehee:
    Yeah I was thinking, its alright as long as the symbol doesnt represent a specific num eg  \pi or \phi
    lmao seems like something you'd do, this means I can casually make:
    \sqrt{a^2+b-\frac{c^3}{7}}= or Random Maths Shiz=

    I will do so if required when joostan gives me that problem
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    (Original post by Felix Felicis)
    Too true! Lambda is one sexy letter :coma: I use a curly w sometimes, don't know why, just do, it looks cool :teehee: Like w
    Agreed. I prefer lower case omega (the curly w to which you refer) more than upper case as well.

    What modules are you actually sitting this summer?
 
 
 
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