Logarithmes

loga (x) = logb (x) / logb (a)
loga (x) = log10 (x) / log10 (a) = ln (x) / ln (a)
ln (x) = log10 (x) / log10 (e)
log10 (x) = ln (x) / ln (10)

loga (x.y) = loga(x) + loga(y)
loga (x/y) = loga(x) - loga(y)
loga (xy) = y . loga(x)
   d'où on tire
    xy = ay . loga(x)
    xy = 10y . log10(x)
    xy = ey . ln(x)

d[ ln (u(x)) ] = u-1(x) . du
d[ ln (x) ] = dx / x
d[ loga (u(x)) ] = u-1(x) . loga(e) . du

log(x) dx = x . log(x) - x
ax . log(a) dx = ax
xp . log(a.x) dx = xp+1/(p+1).log(a.x) - xp+1/(p+1)2     avec p ¹ -1
(log x)2 dx = x.(log x)2 - 2.x.log x + 2.x
(log x)n dx = x.(log x)n - n.(log x)n-1 dx
(log x)n/x dx = (log x)n-1 / (n+1)
dx / log x = log(log x) + Si=1i=¥ [(log x)i / (i.i!)]
dx / (x.log x) = log (log x)
dx / [x.(log x)n] = -1 / (n-1) / (log x)n-1
xm / (log x)n dx = - xm+1 / (n-1) / (log x)n-1 + (m+1) / (n-1) . xm / (log x)n-1 dx
xm . (log x)n dx = xm+1 . (log x)n / (m+1) - n / (m+1) . xm.(log x)n-1 dx
sin (log x) dx = x / 2 . [sin(log x) - cos(log x)]
cos (log x) dx = x / 2 . [sin(log x) + cos(log x)]

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