98 
MEMORIAfc CIENTIFICAS I LITERARIAS 
y = x arc cos x + 
[ x d x 
x+ = 
JVl-x* 
x arc cos x 
]/l — x 
4. / arc tg x d x . 
u == arc tg x 
d x=d x 
• . du = 
dx 
x + x : 
V = X 
y = x arc tg x d x — f • 
x dx 
1+x 2 
= x arc tg x — — L (1 + x ‘ J 
(Humbert, I. 429) 
5. y arc cot xdx = x arc cot x + L (1 + x 2 ) 2 
6. / arc sec x d x=x arc sen x— L (x + ]/x* — l) 
7. / arc cosec x d x=x arc cosec x-j-L (x ]/x 2 — l) 
8. / arc vers x d x=x arc vers x- 
x d x 
]/ 2 x— x- 
x d x [ — x + 1 — 1 
]/2 2 
X X' 
] 2 x — x 
d x = ]/2x — x 2 — arc versx 
. • . / arc vers x d x=(x — 1) arc vers x + ]/2 x — x- 
(Brahy, 33) 
9. / (1 4 - tg' 2 x) d x— /dx+/ tg 2 x d x . 
ta 2 x 
sen- x 
cos 2 x 
sen x d cos x 
cos 2 x 
