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    hi guys, im quite stuck with this question. please give me some hints.
    integrate[((x^2)-(1/x))^4]

    i've tried to let u=the whole thing inside, but unfortunately i don't know how it works.
    thanks
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    I think I'd just multiply it out and then integrate.
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    by binomial expansion? i thought of that before but i think it would be quite time consuming...
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    (Original post by kingsclub)
    by binomial expansion? i thought of that before but i think it would be quite time consuming...
    It really doesn't take long if you do it instead of thinking about doing it.
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    (Original post by Get me off the £\?%!^@ computer)
    It really doesn't take long if you do it instead of thinking about doing it.
    but will it work using the substitution method? cause i want to try that method.
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    bump
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    binomial expansion is the best way to go in this case!
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    I just did it, all the x^2 and 1/x are different functions, both being in the bracket of the power of four.
    The way I thought of it was to say what 1/x is the same as, as a simpler indice, and then applying one of the laws of indices to expand the whole thing.

    Alternatively, what might be a better way is use the chain rule. Add one to the power, divide by the (new power times the derivative of the brackets)
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    (Original post by kingsclub)
    but will it work using the substitution method? cause i want to try that method.
    If you insist on using a substitution.

    Put the term in brackets over a common denominator.
    Use u=x^3+1 as your substitution.

    It would be useful practise as you'll require polynomial division, use of partial fractions, a non-trivial (but not difficult) change of variable, practise on fractional indices, and will probably be challenged to show that it gives the same result (I've only worked it partially through, but it looks doable.).

    Have fun!
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    (Original post by mckinnon94)
    IAlternatively, what might be a better way is use the chain rule. Add one to the power, divide by the (new power times the derivative of the brackets)
    I'm not totally sure what you mean by the last paragraph, but it is NOT generally true that \displaystyle \int f(x)^n \, dx = \frac{f(x)^{n+1}}{(n+1)f'(x)} + C.

    E.g. \int (x^2)^3 \,dx = x^7 / 7 + C (obviously).

    By the fallacious "rule": \displaystyle \int (x^2)^3 \,dx = \frac{(x^2)^4/4}{2x} + C = x^7 / 8 + C.
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    wow, partial fractions !? something beyond my ability then... i stick to the expansion method then. thanks guys
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    (Original post by kingsclub)
    wow, partial fractions
    Only probably, I didn't work through all the details.
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    Have you got an answer for it? I think I have a solution but not sure if it's right?
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    (Original post by elementsofsuccess)
    Have you got an answer for it? I think I have a solution but not sure if it's right?
    http://integrals.wolfram.com/index.j...4&random=false
 
 
 
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