Determine: (4/x-x/4)dx?

U substitution and intergration. Please show how you get answer.

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  • 1 decade ago
    Favorite Answer

    4lnx -(1/8)x^2+C

    Source(s): By thinking for a microsecond.
  • 1 decade ago

    Let u=x/4, so that du = (1/4)dx. The original expression then becomes (1/u - u)(4du) = (4/u - 4u)du. Integrating this, you get 4ln|u| - 2u^2 + C. Substituting u with x/4, the answer is

    4ln|x/4| - 2(x/4)^2 + C,

    => 4ln|x| - 4ln4 - 2(x^2/16) + C

    => 4ln|x| - (1/8)x^2 + C

    since -4ln4 is a constant also.

  • 1 decade ago

    t = x/4 => dt = 1/4dx

    (1/t - t) = Ln(t)-t^2/2 4dt

    =4Ln(x/4) - x^2/8

  • 1 decade ago

    = int (4/x) dx - int (x/4) dx

    = 4lnx - x^2/8 +c

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  • Anonymous
    1 decade ago

    E=(mC)(mC)

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