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Integration by Substition

  1. Sep 27, 2011 #1
    1. The problem statement, all variables and given/known data
    [itex]\int \frac{-2x}{\sqrt[4]{x+2}}dx[/itex]

    3. The attempt at a solution
    [itex]=-2*\int x(x+2)^{\frac{1}{4}}dx[/itex]

    Let [itex]u=x+2[/itex].
    Then, [itex]u-2=x[/itex],
    and [itex]du = dx[/itex]

    .. Continued from above,
    [itex]=-2*\int (u-2)u^{\frac{1}{4}}du[/itex]
    [itex]=-2*\int u^{5/4}-2u^{\frac{1}{4}}du[/itex]

    Is that last step allowed?
  2. jcsd
  3. Sep 27, 2011 #2


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    Yes, absolutely. You are doing it exactly correctly.
  4. Sep 28, 2011 #3


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    Except the exponent (1/4) must be negative since the factor (x+2)^(1/4) was in the denominator in the OP.
  5. Sep 28, 2011 #4


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    Ack. Missed that. Sorry.
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