IZ 4

CAPUT V.

I.^x m+2 ex(a+yx 2 ) p:

306. Problema.

Bato integrati _/x m ex (a + yx 2 ) p invenire integratia /x n ' +2 £x(«+yx 2 )r’,/x m £x(a+yx 2 ) p + 1 .

Solutio.

Primum invenies, fi in (261. §. I.) ponas /3t=o, et m+i loco m:alterum vero obtinebis ex (261. §. III.) pofito /3—o, etm+i loco m.

,_ x"'+^>+yx 2 )p^ rm+o « ,

■yim+2p + 3,; y m+2p+3 / ) *

307. Corollarium 1.

Si in prima formula ponatur —m loco m, et in fecunda —p loco p,prodibunt inde fequentes formulae.

J / '‘sx(a+yx 2 'i p (g+y\ a ) p + I . yf2r'+3—m) PeK(oc + y x 2 '' p

J x m (m—i)*x m-1 ' (m — ia J x m ~ 2

XI / x ' 11gx _ _X m + I _( m+3— 2'.) x n *sx

y^a-{- yx 2 ) p 2a(p—l y (a+yx 2 -) p '~ I 2a(p—1) J ^a+ yx 2 ) p ~ 1 *

308. Corollarium 2.

Ex (306. §.) obtinentur fequentia incegralia, per integrale /s x+ yx 2 ) ex (289. §.) notum determinata.

x 2 " -1 (2n — i)ax 2n, “ 3

yx 2n ex/ (a+yx 2 ; —

2 n + 2. y

■ 2n + 2) 2 ivy 2

. (2n— i) > 2n —3'-.« 2 .x 2n 5 _ ,

”* (2n+2;2n(2n — 2) y 3

(20 + 2)20(211— 2) -6 . 4 > y" y v v y

T (2 n-x) C 2o-3)- 5 - 3 -I-»" A A , . , x «

T i2u+2)2nC2n —2)-6.4 y” + )•

An ,x/(a'+ yx 2 )-, = 1 p/X*±

J V V2u + q + 1 ' (2n+ q +i;(2n+q-

•o

1 q (q—2> 2 y (a+yx 2 )-i - 4 _,

”* (2n+q+l);2i.+q—l)(2a+q—3)

q-3 >

1 q(q—2 Xq— 4) - 7-S-« 2 V a+yx 2 V J ^„ +,

' r (2n+q+I,,(2o+q—l y --- (.211+6X2U+4A ‘

+