\

C A P V T III. 89

C o r o 11. i.

r29. Si capiamus x negatiuum, vt ütdyz—s,eodem modo patebit efle :

1 / \ 1 x X 1 X* X*

Xj — lü a — 2 a* ja J 4 a* etC.

hisque combinandis:

l{aa-xx) — ila—£§ -

sc6

4 a*

— etc. et

/ U "f” A 2 X a x XV . I <* X'* | .

<f^c— a H- s a* -r- J^S- 4- 75F 4- etc.

r

o o r 0 1 I. 2 . '

iZO. Hae potieriores series eruuntur per inte-grationem formularum

= et .

C*

a« '

a a — x x2 a dx

2 Q u JC j f r

ca— xx — 2,sl«*X[ aa I "

«x , JC 4

a 4 *“r

4- etc.)

Est amem ss,’-=~=t(aa-xx)-l aa et s&g-.-lg*,ita Yt iam his formulis- per series integrandis super-sedere possimus.

Exemplum 2 .

iZi. Formulam dijserentialem a g^ x,per seriemintegrare. 1

Sit dyzz r ~~- i et cum fit j = Arc tang.f-,idem angulus serie infinita exprimetur. Quia enimhabemus:

a

• xx — a

X X x 4

a s **+• q 5 a 7

erit integrando:

Are. tang.^3

* -^4.-^_^ , Pfr

( p— 3 fl 3 *^P 5 tfi f & » Cll«

M Exem-