U-Substitution?

Use U-Substitution to evaluate

5x / (x-2)^1/2 dx

3 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    Let u=x-2. Then, x=u+2 and dx = du

    Then,

    \int 5x/(x-2)^(1/2) dx becomes

    \int 5(u+2) * u^(-1/2) du=

    5\int (u^(1/2)+2 u^(-1/2)) du=

    5 (2/3 u^(3/2)+ 4 u^(1/2)+C=

    5 (2/3 (x-2)^(3/2)+ 4 (x-2)^(1/2)+C=

    I hope this helps! :)

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  • 1 decade ago

    put

    x-2=z^2

    then

    dx=2zdz

    x=z^2+2

    the problem now reduces to

    (z^2 + 2)/z 2zdz

    that is 2*(z^2 + 2)dz

    that is (2/3)*z^3 + 2z + C (integrating constant)

    now put the values of z

    (2/3)*(x-2)^(3/2) + 2*(x-2)^(1/2) + C Ans.

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  • 1 decade ago

    I think that Max P is the one with the right answer, because he took dz for consideration, and organised that data in equations properly.

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