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integration problem using substitution watch

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    ok, i think i may be being very thick, but i've been running through my 1st term problem sheets (doing biochem at ox), and i can't figure out this integration. it says to do it by substitution... y=x^3(x^4 + 4)^2. Any help anyone? Please no one do it by parts and show me that, has to be substitution! x
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    (Original post by onlywee)
    ok, i think i may be being very thick, but i've been running through my 1st term problem sheets (doing biochem at ox), and i can't figure out this integration. it says to do it by substitution... y=x^3(x^4 + 4)^2. Any help anyone? Please no one do it by parts and show me that, has to be substitution! x

    Can you not multiply out the brackets and integrate each term separately to give:

    1/20*x^20 + x^8 + 4x^4.
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    need to be using substitution...thanks though
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    (Original post by Ralfskini)
    Can you not multiply out the brackets and integrate each term separately to give:

    1/20*x^20 + x^8 + 4x^4.
    Thats what I would do.

    You do biochem and you study maths? I didn't realise. However I study Mechanical Engineering and all we do is maths. Its pisses me off when people think we learn how to fix cars or something equally stupid.
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    yep, bugger loads of maths! i knew it'd happen, but i'm hating it way more than i thought i would!
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    this is pretty easy.

    int. x^3(x^4 + 4)^2 dx

    let u = x^4 + 4
    du/dx = 4x^3
    dx = 1/(4x^3) du

    subst. for dx.

    so int. (x^3)/(4x^3) u^2 du = int. 1/4 u^2 du = [1/12 u^3]

    = 1/12(x^4 + 4)^3
 
 
 
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