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# integration problem using substitution watch

1. 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
2. (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.
3. need to be using substitution...thanks though
4. (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.
5. yep, bugger loads of maths! i knew it'd happen, but i'm hating it way more than i thought i would!
6. 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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