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    can anyone help me with this integration question:

    use the substitution u=x^(1/2) to find the integral of 1/x+x^(1/2)
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    (Original post by joyndlovu)
    can anyone help me with this integration question:

    use the substitution u=x^(1/2) to find the integral of 1/x+x^(1/2)
    Have you used the substitution? What did you end up with?
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    Do you know how to use substitution?
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    (Original post by B_9710)
    Have you tried anything, if so it's helpful to post what you've done so far
    I've found out that u^2)=x making my new integral
    1/u2+u dx but I'm having trouble of finding du
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    (Original post by joyndlovu)
    I've found out that u^2)=x making my new integral
    1/u2+u dx but I'm having trouble of finding du
    Differentiate u=x^1/2 leaving you with du/dx=1/2x^-1/2 and then go from there
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    (Original post by Rajan17)
    Differentiate u=x^1/2 leaving you with du/dx=1/2x^-1/2 and then go from there
    How would you get du by itself?
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    (Original post by joyndlovu)
    How would you get du by itself?
    Take the dx over by multiplying both sides by dx and then take the 1/2x^-1/2 over by dividing by it (sorry of that makes no sense) but you should then end up with 2x^1/2du=dx (I think)
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    (Original post by joyndlovu)
    How would you get du by itself?
    You don't want du by itself, you want dx by itself because that's what you're aiming to replace.
    You have u^2=x so then by implicit differentiation 2u \dfrac{du}{dx} = 1. Multiplying both sides by dx yields 2u .du = dx as required.

    Often neater than dealing with fractional indices.
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    I got this:
    u = x1/2, so x = u2

    dx/du = 2u, du/dx = (2u)-1

    integral of 1/x+x(1/2) dx = integral of (1/u2 + u)du/dx du

    = (2u-2)/-2 + u/2 + c

    = -u-2 + u/2 + c
 
 
 
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