125

Polito z~bx + a fiet 7-7^- —

CAPUT V.

293. Corollarium 6.

tz/(z + a)

X 5 « X

b*

— b x ■

e z — a

/( z + a )

zb 2

adeoque

bx 4 - s

ez

Z / (z + »)

Eapropter, fi integrale algebraicutn primae partis capiatur per(241. 248. § )» et pars altera integretur per (291. §.)• prodibunt fequert-tia integralia.

y _ n 2 _ \f a /-bx4-a -f-2^abx ^ ,

bx—a b b^b ^ bx—a J

y r 'x 2 fiX _

bx-fa

2 x

Arc Cofin 3

-b x

b b^b a + b x

293. Problema.

fC.

Integrari exponentes differentiales e x/\X k ,

£ x

x/X k

£ X

/X k ' X ' x/X kpro quovis numero integro impari et pofitivo k, et quolibet trinomio« + / 3 x + yx 2 =X.

Solutio.

Ponatur in (262. §. TI.) q—invenietur sequens formula (I) et(IT). Porro fiat in (261. §. III.) m = o et p = + S; obtinebitur fequensformula (III) et (IV)» Cum pro nt^j pars fecunda primae formulae fiat

aequalis nihilo; erit integrale exponentis differentialis P ro *I uov i s

numero impari pofitivo k >1 perfefte algebraicum, licet id pro k“i fitloganthmieum, aut trigonometricum (286. §.): invenietur vero illud

ope formulae (I), fi in hac fiat fuccelfive n:=3, n— 5, nt= 7-nn=k.

Secunda autem formula, fi in ea ponatur fuccelfive n= 3 I, n — 3 » n — 5 »- — nt=k—2, dabit integrale fsxy OC k pro quovis numero impari pofitivok dependenrer a noto integrali J'efX( 288- §-)» Pari ratione, fi fiat

n — — i. n=:i, n —3, n —5.-n — k — 2/ invenietur integrale

n 6 ' rk

J ---- ope tertiae formulae, dependenter ab notis integralibus

(286. 290. § ). Formula quarta demum dabit integraleQ 3 expo-