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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 182r, page id 00068196:0359
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(3tio
X = y. X logX = log y se dx  logx. dx = dy: y
o
(2d0)
Ergusq )3 dx = y logx. dx =dy seu Sydx + sylogxdx = y
seuto) X dx + fx. lag. X dx = y. Itaque haec duo
Summulida ex se invicem pendent X. et X logX
X-1
tx +
Ex aeq. 3 fit 1+ log. X tadu 
ymo) dy: ydx. SebxXC Unde si ddx - 0, fiet
a, X. logk
d log. X =Add log y: Ax san dxdX 1X = se seu dx dloyr dtle
seu ex dogla axdlogx = dd log. y. sed hoc
81ox
misso ex g. sufficit ex ∞g. 3 haberi dX. = X. dx + X. bge dp
A
t
F jam d, X. logX. fit = (9n0) X= 1, + logX. X. ex + logx x. dx
quaeratur
quaeratur puline rixte,
log. sia
r-
o)te
X = P. l0g. X
+ log.X
generaliter X = y fit Y logx = log y. et  vdx. X FlogXdi
out
dy: y seu d. X. = E V V eB V. X. dx + X. log. X. do
10mot
Xtc
aXte s
d. X. l0gX = Rdx, 1.X = log. X
r-1
4
= dx, r. X log. X - + log. X. XtC. X
XtCj  x+
1
te ure
+ o. X. (Xt C. X. +X. bgp
1-
+P-1
X
dx, Y. A. log. X. +(0g. X. X. + legx X
e
+k. 10g2. 
e + XV
lgs. X
e
H
d.X  = _dx, X. + X? log. X quod et jam pat et ex aeq.
si Y et e =0 fit
 x X,  2
si r = 1 fit et C= 0 fit   d, X. log. X = dx, X. + logX. X + X. logX
sed Ergo. fX. log. X dx=
d. X∞. 1.
X logX. dx + XC dx = 1. X lx
fiet di
d, X = X axF X log. X dx + X dx + 0. X dx
+-
d. X.
12
d) X. =
d, qute -
d, X2  sogX. =
X2F log. X dx + X dx +, X. dx
X log. X de + XF ax + 2 X dx
ure
Xte-
XEB log.X dx +R. dx +e X
X
logX X. dx +log. X. F7
+
t
At
logx
dx
+1
X ulgx
xte- dx
mp