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

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

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- mathematicianLv 71 decade agoFavorite 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.

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- Anonymous1 decade ago
E=(mC)(mC)

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