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Homework Help: U-substitution problem

  1. Jun 24, 2015 #1
    1. The problem statement, all variables and given/known data
    Evaluate the integral using usub

    int(x*sqrt(1+x)dx) from 0 to 8
    2. Relevant equations

    3. The attempt at a solution
    Okay, so I attempted to set for u sub

    U = x+1
    u^2 = (x+1)^2
    2u*du = 2(x+1)*dx
    u*du -1 = x*dx

    I got this far but I don't understand what to do with this, because of the (-1), separate from the u*du
  2. jcsd
  3. Jun 24, 2015 #2


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    There is no reason to square u.
    Just take the derivatives, du = dx, x = u-1. Then you have a normal polynomial in u.
  4. Jun 26, 2015 #3


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    Gold Member

    Slight nit-pick -- it isn't actually a polynomial though it does only have terms of the form ##x^p##.
  5. Jun 26, 2015 #4

    Ray Vickson

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    In the "Geometric Programming" literature, it would be called a "signomial". (It would further be called a "posynomial" if all its coefficients were ##>0##.)
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