Calculus

Evaluate the function below from x = 1 up to x = 4.


∫(7−lnx(x)(3+lnx))dx

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asked by Kevin
  1. Suspicious of your typing, especially the lnx(x) part

    Sent it to Wolfram and they read it as:
    https://www.wolframalpha.com/input/?i=%E2%88%AB%287%E2%88%92lnx%28x%29%283%2Blnx%29%29dx+

    https://www.wolframalpha.com/input/?i=%E2%88%AB%287%E2%88%92lnx%28x%29%283%2Blnx%29%29dx+%2C+from+1+to+4

    Wolfram uses log for ln

  2. To integrate lnx or x lnx, use integration by parts

    u = lnx, du = 1/x dx
    dv = dx, v = x
    ∫lnx dx = x lnx - ∫1/x * x dx = x lnx - x

    If
    u = lnx, du = 1/x dx
    dv = x dx, v = 1/2 x^2
    ∫x lnx = 1/2 x^2 lnx - ∫1/2 x dx = 1/2 x^2 lnx - 1/4 x^2

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    posted by oobleck

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