188 
etc. 
cujus expressionis valor est logarithmus hyperbolicus nu- 
meri 2, scilicet Î EE ; si peracta integratione X — 1 as- 
sumitur. 
Exemplum Il 
m m 
$. 7. Integrare formulam dy —0xY (1+ x"). 
Solutio. 
m MALE 1 M (ses DU (m—1)(om—3) ,3m 
{+2 tre Du 2m Fe TX Me 
 Gm—i)tam—1)Gm—:) xt" 
| GMT TOR à AM NME 
Proinde 
dy=dx+E x" ox == DS 0x + Mr x" 0x — etc. 
hinc, si constans PAPE — O statuatur , 
x +1 (m—1)x2Mm 71 D Ree 
PSE te) 0 emenr) 0 ne many) 
(m—a1)(am—:1)(3m—2) x 
amant) — —- etc. 
mCy—x) __ (mi) am | (m—i)(am—i)am 
vel RME mi TT enGmn) À T2 m(gmi) Mis 
vel tandem, \positis "—%, et "0 —Y, 
2e (m—i)z (m—i)(am—i)2  (m—1)(2m—s){gm—1)23 
ET ete) 2.3. m2(3m+1) 2. 3. & mIi(4mti) "pete, 
haec series, si z fractionem admodum parvam, m vero 
