ET MÉTUODES DÉVALUATION DES INTÉGRALES DÈFINIES. 111. lM'^ 17. N\ 5, G. 



/■" Sin.^x dx C^ Sin.'^ic.Tanq.x djo ['" Sin.^x.Sin.-iiodx 



I :; ,-(790), = ƒ ~ ,.ndi),=zl ^ ,.(792),= 



o "o "^0 



("^^Ail^^^Éz^l ,E-(,) + (^-^^^ni-P !)^ 'rji.,..Cos.^ dj. _ 



ƒ 1/(1— p2Cos.%-) -óp* ^"^ 3p*- ^^th y'll—piCos.^^c) .X ^ '' 



o o 



ir 



o o 



ƒ'" Sin .a-.CosAx dx ■ ^ ƒ■" Siri. x. Cos.^ x dx 

 ^/ (1 Z72 a,s:2^) 7' ^'^■^^^' ^ / 1/(1— p2Cos.2.r) 7' ^^^^^' ^ 



o -o 



/■2" (?os.4a;(/:» 2 1 +«2 1 



6. Ou trouve ensuite par ces uièmes formules : 



i''" Sin.'^ X dx ƒ■" Sin. X. Cos. X dx 



J [/{l—p^Sin.^x)^~^' ^^^^^' "" j 1/(1 



■ p2 &V(.2 ^)3 ^ 



5ïVi. X. Si'n.2 § .« d^ f^ Sin.^ x dx 1 1 



(798), 



C Sm. X. Sin.^ z X dx f^ Sin? x dx 1 1 ^, 



^ ^j \/{\—p'^~SÏiJxf x' ' ^^''^^^' ^ j \/ [l—p''- Sin? xf ^p(l— p2) ^^'^~pi^ ^^'^' 



ü 



ƒ" Sinje_^ dx ^ p Tang.x dx f^ da; 



J \/{^—V- Sin? xf .r ' ■ ^ / ^/(l— p2&-«.2^)3 -y ' ' ^ ^' ~ ƒ j/ (i _ p2 ^^„.s ,^.)3 "~ 



|> o o , 



1 1"^ Sin. X.Cos. X dx f'" Sin. X.Cos? X dx 



~ l_p2 (?')' / ^/(I_p2,9i„.2^j3 P ■ • ^^'^~'' = ƒ V''(l— P^'«.2.r)3 7' ■ ■ ^*^^^^' "" 

 O O 



TT 



ƒ2 Cos.2.j;d/j; 1 /"" &■n.3.^• Ja; 

 7(r-rpï5i;j^ = j^ (F'(p)-e'(,)), / t^p^t-^^' ^''■'^' = 



ü "o 



n 



ƒ"■ Sin. X.Cos. X d.v /'"' Sin. .t. Sin? ^x dx f 2 Sin?xdx 

 —- — ,.(805), =2 ƒ ,.(806), =ƒ = 

 \/{i—p^Cos.-Kv)^ x' ^ " I 1/(1— p2Cos.2./)3 a,' ^ ■" J y/(l—p2Cos?x)i 



o o 



1 ,^. , ^, , /"^ ASi'n.a; dx , /■* Tang.x dv 



~{F'{p)-E'(p)}, / — — ^TT^— - -(807, = / ^- — ^rT-,3 - ' ■ (SOS), = 



3'' y 1/(1 — p^tos?x)^ X J \/(l — p^Cos?x)^ X 



P 

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