162

caput rr.

adproximare ad radices numerorum, quorum perfeftae radices nequeantafiignari.

360. Corollarium i.

Si funftio X—^(ax m + bx n )~(ax m + bx n )' s juxta (54. §.) explice-tur per seriem, obtinebitur per (249. §.) sequens notatu dignum in-tegrale.

/«x/(ax m -4-bx n ) c=;

12

i

• x 2m + 2

+

in-m+Jb.x L

75

2 a (2N—m+2)

411-3 m + *i.b 2 . x i

2. 4a 2 (4n—3 m+2)

6 n - $ m + x 8 n - 7 m + 2

. r.Zb'. x _2___ i. 3.5 b 4 . x 2

* x 7 '

2.4.6a 2 (6n — 5m+2) 2.4.6.8 a* (8n—7m + 2)

+

• rn-(2r- l)m + 2

+ 1 • 3 • 5 • 7-(2r— 3>b r .x 2 _

2.4.6.8 -2r.a“ (2rn—(2r—1) m + 2)

Terminus ultimus, utpote r tus, dabit fingulos, poft primum ordinesequentes, terminos, fi loco r termini seriei 1, 2, 3,4, 5, etc. fucceflivefubftituantur.

361. Corollarium 2.

Et fi Xr=(ax m +bx n ) T explicetur per seriem (Z 5 - §); obtinebiturper (249. §.) sequens integrale.

r sx

J

K

' sf (ax ,n + bx“)

—J_ i.b

i ni - 2 +

4. ; m - 2n - 2

(m—2)a". x 2 2(3rn — 2n—2)a .x 2

1.3 b 2

+

1 • 3 • 5 b’

4 * 4 7 m - 6 n - 2

2 4(z rn—40—2)a .X i 2 46(70,-60-2)3 .X 2

±

»»3.5-7

.- - - - - - (2r—i )b r \ + a

arti (aMDm-arn.a J

2 4.68 - - - 2r((2r+i)m — 2rn—a)a a .x 2 y

S c h o«

L