How do I find the integral of a natural log?

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How do I find the integral of a natural log?

eg the integral of ln(3x) ?

2007-05-02 03:53:45 · 2 answers · asked by ? 3 in Science & Mathematics ➔ Mathematics

2 answers

Integral ln(ax)dx is a standard form
x*ln(ax) - x + C so plug 'n play
x*ln(3x) - x + C

HTH

Doug

2007-05-02 03:59:12 · answer #1 · answered by doug_donaghue 7 · 0⤊ 0⤋

Use integration by parts.

u=ln(3x) --> du=3dx/(3x)
dv=dx --> v=x

integral (udv) = uv - integral (vdu)

integral ln(3x)dx = xln(3x) - integral dx

integral ln(3x)dx = xln(3x) - x

integral ln(3x)dx = x[ln(3x) - 1]

2007-05-02 11:07:27 · answer #2 · answered by Astral Walker 7 · 0⤊ 0⤋