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6 March, 19:42

Find a formula for the function f (x) such that f′ (x) = (ln (x)) ^2/x and f (2) = 6

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  1. 6 March, 20:12
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    F (x) = ∫ln²x/x dx = ∫ln²xd (lnx) cause d (lnx) = (lnx) 'dx=1/x dx

    = ln³x/3 + C with C is constant

    In addition, we have f (2) = 6, so we have 6=ln³2/3+C

    or C = 6 - ln³2/3

    And f (x) = ln³x/3 + 6 - ln³2/3
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