D. BIERENS DE HAAN. NOTICE SUR DES INTÉGRALES. 393 
'J-^ sin^ xxos"^ X d X n 
/J-^ sin^ x,^ 
(1 + ^ si 
0 
sin^x.cos^ x)^ 2 y 
, (12) 
/^^ sin'^ x.cos^ X d X n ^^^^ 
/ 
0 
Puis 
^ sin^x.cos^ xdx 
(1 -i- p sin'^x.cos'^ x)"^ 4y 4_|-^' 
sin'^x.cos'^ xdx ^ ^^^^ 
^ (1 s^*^^ x.cos"^ xY 
=-7lV^ F- 1 +2 , (i>> 0), (15) 
=— [-1+ ^ (^+^) ^rmngy^)"] ,(0>i9> -4),(15«) 
rj"^ sin^xxos^xdx tt / 1^ 2 ^ 2+^? \ ^^^^ 
J (l-hi9sm^:r.cos2^r)2~2p\ j) p\/I^p 2^4+^'/ 
/J^^ sin^xxos^xdx ^^^^ 
sin^xxos'^ xV ' 
(1+» sin^xxos'^ xy 
0 
j-TT sin^a^.cos^ xdx 
^ (1 rhi? sin^ xxos'^ x) ^ 
= 9-7TTr^ ["-1+ ^i^^ (^ÎTi^'+l/^)] ,(^> 0),.(19) 
2i?(4+i?) L V>(4+^) -I 
=9^îV-^ \~^+^^^^A.Arcsin{i\/^)] ,(0> ^> ~4),(19«) 
j (1 -\- p sin"^ xxos"^ xY 
0 ^ 
