كل ماستحتاجه في الرياضيات

بسم االله الرحمن الرحيم والصلاة والسلام على أشرف المخلوقين محمد سيد المرسلين وعلى آله وصحبه أجمعين أما بعد ٬ يسرني أن أقدم لكم هذا العمل المتواضع وهو عبارة على ملخصات مع تقنيات الرياضيات لمستوى الثانية بكالوريا علوم تجريبية مجمعة في كتاب واحد وهي للأستاذ حميد بوعيون sefroumathssitevoilafr تجميع وترتيب ALMOHANNAD

ا ی ت وا ل I 1 2 a a a a a a a a 3 a lim f x g x lim f x g x b g x f x g x f x c 0 limx 0 0 f x a a a g x d 0 0 0 0 limx 0 0 f x a g x quot quot e 2 x x 2 2 x x x x x x 4 2 0 0 0 1 cos tan sin 1 lim lim 1 lim 1 x 2 x x ax ax ax ax ax ax 5 amp x0 f amp a limx amp f x limx x0 f f x f x - 0 1 2 f amp b 3amp 3quot 0 3amp -4 6 f f amp 5 x 2 0 amp x limx amp f x limx f x l 2 g f 6 x g x f x x x g x l amp 7 x0 f x l g x a lim 0 x g x x0 f x g x b limx f x x0 f x g x c limx g x x0 g x f x h x amp d 0 0 lim lim x x g x h x l amp II 7 8 a 1 9 7 9 8 b f amp a 2 lim f a b f a f b a f a b f f b amp f amp b lim lim f a b f b f a b a f a b f f amp 3 a b 0 f amp a f b f a a b 0 f amp b f a f b 0 a b f x 0 amp c a b f a f b 0 quot c 9 f amp III amp 1 I 0 f I 0 9 f f I J 0 f 1 f J I amp 1 x J y I f x y f y x a 2 1 f J 0 b 1 f f ltquotamp 3 J 0 9 ampamp c Cf 1 f 6amp amp C y x limx f x l lim x g x limx f x limx f x l c a b f c c a b f c 0 J amp I f

3 1 f I 0 9 f amp x I f x 0 1 f J f I 0 1 1 1 x J f x f f x n IV n x - 1 n IR y 7 x 1 n y x 4 16 2 4 2 0 2 16 و 4 2 16 4 2 16 2 2 a 0 n 0 b n x x c n n n n x y x y x y x y x y lt lt d n n n n x y x y x y x y x y 1 n e n n n n x y x y x y x y x y n f n n n n x y x y x y x y x y 0 g n n n n x x x x n n n x IR x x p n h b a IN n n n a b ab p np p n n n p a a a a n n p np n n a a a a b b b n p np n p a a a i p n n p n p x x x p p n p x x x n quot n x y x y n n xy 0 1 n n n x x y y 2 3 3 x x x 0 3 3 3 3 3 3 3 3 x x x x x x x x 3 3 3 3 2 2 2 2 a b a b a b a b a ab b a ab b 4 4 3 2 2 3 a b a b a a b ab b b a j IR r r r r r r a a a r r r r a a r r r r a a a r r r ab a b 1 r r a a r r r a a b b

ا ت ادی I 1 I U U I n u n 2 n n I U n I U M n M a n I U m n m quot b quot c M m n n I m u M n n I U k 0 n I U k n 3 n n U n U U n n1 a n U U n n 1 amp b n U U n n1 amp c n U U n n 1 amp amp d n U U n n1 e p n u u p n Un 1 p n u u p n amp Un 2 Un 3 u u n n 1 Un u u n n 1 0 amp Un u u n n 1 0 amp Un u u n n 1 0 amp amp Un u u n n 1 0 Un u u n n 1 0 II 1 n n U r n U U r n n 1 r Un a 0 1 21 u u n n 1 3 Un b 0 1 u u cte n n 1 4 3 1 و و 0 c a c b 2 2 a b b 2 un 0 1 r 5 u0 n U U nr n 0 1 u1 1 0 1 1 1 U U n r n 1 u2 1 0 2 2 2 U U n r n U p n وU 6 3 U U n p r n p r 5 5 8 pوn 3 3 Un 1 r 5 u0 0 1 2 1 2 n n u u S u u u u n u0 S 9 un S 9 S 9 n 1 1 1 1 2 2 n n u u u u u n 2 0 1 0 1 1 2 n n u u u u u n 6 3 1 1 2 p n P p n u u u u u n p III 1 n n u q 1 1 n n n U qU q 1 8 1 a 0 1 21 lt Un1 3 1 Un b Un u q u n n 1 4 3 1 cوbوa 0 c 1 2 ac b

2 n u0 0 1 q 5 1 u n n n u u q 1 1 u1 1 0 1 n p u u q n 1 un p وu 6 2 q 5 n p u u q n p 5 8 pوn 3 3 Un 0 1 q 5 1 U0 1 q gt 1 0 1 0 1 1 n n q S U U U U q u0 S 9 S 9 n 1 S u u u n u 0 1 0 1 n q 1 1 0 1 1 0 2 1 1 1 n n q u u u u q q 1 2 1 1 1 n n q u u u u q 6 1 1 1 1 n p p p n p q u u u u q IV lim 1 n q 0 1 1 1 1 lim 1 1 n q q q q q دة quot 2 amp4 U l V n n V n U n a lim 0 lim V U l n n amp4 U V n n V n U n b lim lim V U n n lim lim U V n n amp4 V U W n n n W n V n U n c lim lim lim V W l U l n n n 5 5 Un 3 5 4 U Vn n U V n n V n U n a amp4 V n U n lim lim U V n n b quot amp c U f U n n 1 5 I f n n 1 U I U f U f I I l 5 5 Un I f f l l

I a 1 2 2 z a ib a b 1 وi aوb z a ib z b i 2 i i 1 z quot z a ib c R z a o z amp a Imz b z amp b z a b 0 - z z ib a 0 b a b a 2 a a a ib a ib b b a a ib b II aوb z a ib - 1 z a ib - z z 2 a z z z z z z i b z z z z z z c 1 2 1 2 n n z z z z z z z z z z d 1 2 1 2 n n n n z z z z z z z z z z z z n e 1 1 z z z z z z z x iy f 2 2 2 2 Im z z x R z z z iy i z 2 2 zz x y III aوb z a ib 1 - z z 2 2 z zz a b quot 2 z a z a a z b z ib b 2 2 2 z z z z zz a b z z z z z z 0 0 c d 1 2 1 2 n n zz z z z z z z z z n n z z e 1 1 z z z z z z 2 z zz zz z z z z 2 2 a ib a ib c id a ib c id c id c id c id c d amp IV 56 5 P 2 quot 34 1 2 o e e 1 M z a ib P M x y a aff M u x y b v u 7 z a ib aff u z z M x y z a ib c M z P u x y 7 z a ib d z 2 u z v a 2 1 aff e i aff e aff o 1 0 b z M z x ox z M z ox z M z x o c z i M z y oy z i M z oy z i M z y o quot 2 a aff M aff M M M aff MM aff M aff M MM aff M aff M b aff u aff v u v aff u v aff u aff v aff u aff u u aff u A B G c 1 aff G aff A aff B AB- I d 1 2 aff I aff A aff B 78 9 C B A e c B A z z z C B A A B C A B A z z z z

- amp V 1 8 z M z z 1 e OM arg z arg 2 z e OM 1 arg 0 2 arg 2 arg z z z z z z k arg 2 2 arg 2 2 arg 2 z i z z i z z i z k z 2 lt arg 2 z z r z r i cos sin quot z r z i z re r r r r 2 و a 3 z a ib b 2 2 2 2 2 2 2 2 2 2 cos sin a b z a ib a b i a b a b a b i a b cos sin cos sin i i c cos sin cos sin i i cos sin cos sin i i sin cos cos sin 2 2 i i 4 1 1 n n r r rr r r n r r r r r r r r arg arg arg 2 arg arg 2 arg arg arg 2 1 arg arg 2 arg arg 2 n zz z z z n z z z z z z z z z i i i e e e n i in e e i i e e i i i e e e 1 i i e e 1 i e 2 i i e 2 i i e 5 1 arg 2 arg arg 2 e u aff u u v aff v aff u 1 arg 2 arg 2 B A D C B A e AB z z z z AB CD z z 1 C A B A z z z z 1 arg 0 2 C A C A B A B A C A B A AC z z z z AC AB AB z z z z z z AB AC z z Moivre quot 6 cos sin cos sin n i n i n Euler quot 7 1 cos 2 1 sin 2 ix ix ix ix x e e x e e i 2cos 2 sin ix ix ix ix e e x e e i x 4 7 gt 1 2 1 i i z e z e 1 2 cos sin cos sin cos cos sin sin 2cos cos 2sin cos 2 2 2 2 2cos cos sin 2 2 2 i i z z e e i i i i i 1 2 cos cos sin sin 2sin sin 2cos sin 2 2 2 2 2sin cos sin 2 2 2 z z i i i A 2 2 2 2 1 2 2 2cos 2 i i i i i i z z e e e e e e 2 2 2 1 2 2 2 sin 2 i i i i i i z z e e e e e e i - 01 VI 1 z z z n n z Z 2 n a z a Z r 3 A Z 2 01 1 n k k z r k n n n n A 1 4 2 1 k k w n k n 01 1

01 5 a Z r Z 2 2 Z r r Z 2 u r u 1 b 02 1 Z a 2 Z a a u u a Z 02 2 Z a a 2 2 2 Z a i a i a u u i a Z 02 33 Z ib b 2 2 2 2 1 1 2 2 2 b b b Z ib i i i 1 Z 2 b u u i 02 4 Z ib b 2 2 2 2 1 1 2 2 2 b b b Z ib i i i 1 Z 2 b u u i b 0 0 وa Z a ib 02 5 Z i 3 4 z x iy B 2 2 2 z x y ixy 2 2 2 2 Z 5 z x y 2 2 2 2 2 2 2 3 1 2 4 2 5 3 x y z Z z Z xy z Z x y quot E 3 1 2 x 1 quot x 1 2 2 x quot E 3 1 2 2 8 y 2 y 4 y 2 quot y 2 quot G 4 7 y وx xy 2 0 2 9 1 2 x y quot 1 2 x y u u i 1 2 Z II 1 4 VII quot 2 a 0 az bz c 0 B 2 b ac 4 9 0 H1 2 b z a u وu 0 H2 9 2 b u z a 2 b u z a 2 a 0 az bz c 0 2 1 z وz 1 2 1 2 b z z a c z z a 2 a 0 az b z c 2 0 quot b ac 7 0 H1 b z a 9 7 0 H2 1 2 b u z a 2 2 b u z a u

I quot 1 f a 0 x limx x f x f x l x x f x l 0 f b 0 x lim x x f x f x l x x f x l d f c 0 x lim x x f x f x l x x f x l g f d 0 f x 0 x d g 0 0 f x f x 2 quot cf x0 f a amp f x 0 M x f x 0 0 T T y f x x x f x 0 0 0 quot Cf x0 f b amp f x d M x f x 0 0 T1 T y f x x x f x 1 0 0 0 d amp c d lim x x f x f x x x f 0 x Cf - quot 0 0 A x f x e lim x x f x f x x x f 0 x Cf - quot quot 0 0 A x f x f lim x x f x f x x x f 0 x Cf - quot quot 0 0 A x f x g lim x x f x f x x x f 0 x Cf - quot 0 0 A x f x amp quot Cf x0 f 3 M x f x 0 0 -amp Cf x0 f 0 0 M x f x 3 f I g I f I g f x I g f x g f x f x quot 4 I quot f x I f x 0 1 f J f I 1 1 1 x J f x f f x quot 5 amp I quot amp u a amp n D x u x f 0 f x u x amp 5 x0 4 4 amp f b 6amp amp 0 f amp x 0 x 4 quotamp quot 1 a a 0 f g f g 12 af af 13 x 1 2 f g f g fg 14 ax a 3 4 r r 1 r x rx 15 r r 1 f rf f 2 5 1 1 x x 2 16 f f g g f g g 6 1 2 x x 17 2 1 f f f 7 2 u x u x u x sin cos x x 18 8 3 2 3 3 u x u x u x cos sin x x 19 9 1 n n n u x u x n u x 20 2 2 1 tan 1 tan cos x x x 2 10 1 tan 1 Arc x x 21 sin cos u x u x u x 11 2 tan 1 u x Arc u x u x 22 cos sin u x u x u x 23 2 tan 1 tan u x u x u x

6 I quot amp f I amp f a x I f x 0 I f b x I f x 0 I f c x I f x 0 - 7 f amp I quot amp f 0 8 9 4 6amp f amp x 0 x quot 8 I quot amp f x I f x 0 quot quot amp Cf a x I f x 0 quot quot Cf b -quot - 9 I quot amp f x I 0 0 f M x f x 8 9 4 6amp 0 x amp x0 8 9 4 3 6amp f a 0 0 lt M x f x quot amp 5 ampamp amp5 b gt amp f x II 1 Cf quot x a 6 a 2a x D f Df xquot 2 f x D f a x f x Cf quot a b b 2a x D Df xquot 2 2 f x D f a x b f x 1 2 quot a quot gt 3 quot Cf limx a f x lim 5 x f x b lim 5 x f x 1 2 b lim 1 x a f x quot x a 6 a Cf lim 2 x f x b quot y a 6 Cf lim 3 x f x 6 limx f x x a limx f x x lt quot Cf b lim 0 x f x x quot lt quot Cf c lim 0 x f x a x lim 6 x f x ax lim f x ax b i quot y ax b 6 Cf lim f x ax ii lt quot Cf y ax amp quot y ax b 6 Cf lim 0 f x ax b y ax b 5 lt quotA B lt quot f x ax b h x quot f x 5 lim 0 x h x amp quot 3 Cf quot5 lt f x m amp quot a y m 6 Cf quot5 lt f x 0 amp quot b quot Cg Cf quot5 lt f x g x amp quot c 3 lt f x g x quot d gt Cg Cf 6 y ax b 6 Cf C amp quot5 e f x y 8 amp amp Cf f x y 0 amp Cf f x y 0

I o i j k v x y z u x y z 1 2 2 2 u x y z u v xx yy zz quot 2 B x y z B B B A A A وA x x z AB x x y y z z B A B A B A 2 2 2 AB x x y y z z B A B A B A quot 3 n amp P amp amp P a P D amp P ax by cz d 0 b n a b c amp P amp quot amp c A1 1 2 P amp amp n 21 1 amp amp M x y z P AM n 0 1 quot 1 2 1 1 0 2 1 2 1 1 2 0 x y z x y z P x y z 2 1 0 n 21 1 2 quot P amp P amp A P 1 1 2 2 1 0 x y z - P x y z 2 1 0 d 1 2 1 2 0 d quot d u a b c D وD v a b c u v quot D D u v 0 aa bb cc 0 quot e u D i w وv P quot D P u v u w u v u w u a b c D ii P n amp n وu 1 quot D P a a b b c c u n 1 quot D P u n 0 2 P D iii P amp D amp amp D amp P amp amp f n Q وP i n n n quot P Q n n 0 n quot P Q n P ax by cz d 0 ii Q a x b y c z d 0 aa bb cc 0 quot P Q quot g ampquot A P i P A quot H P A amp AH amp d A P AH P ax by cz d 0 ii ampquot 0 0 0 A x y z 0 0 0 2 2 2 ax by cz d d A P a b c II M quot amp 3 r - 34 amp 1 M r 5 3 r - a b c 34 S amp amp 2 2 2 2 2 x a y b z c r - amp - 2 2 2 x y z x y z 0 n P D n P A M n P u D n P D P H A

amp 3 2 2 2 0 x y z x y z quot 63 amp ampquot amp 7 1quot 2 2 2 d c b a 2 2 2 a b c d 2 2 2 2 a b c d lt 0 2 2 2 a b c 2 a b c d 0 2 2 2 a b c 34 amp 2 a b c d gt 0 - 2 2 2 r a b c - amp 2quot 2 2 2 x a y b z c k amp3 ampquot amp 2 2 2 2 2 X X X 2 k lt 0 a b c 2 k 0 r k - a b c 2 k gt 0 - 4 63 S amp 9 AB 3quot8 amp S quot 1quot 0 0 A B A B A B x x x x M x y z S AM BM y y y y z z z z x x x x y y y y z z z z A B A B A B 0 2 quot amp9 - 0 A B A B A B x x x x y y y y z z z z 0quot 5 amp P r - 34 amp S a 1lt 63 d d P P S 7quot S 7quot lt P S gt P 2 d r gt 1 i H ampquot quot S P 2 d r ii quot 3 H B quot H S B P amp A3 P C 5 S 7quot P 2 d r lt 1 iii quot H 3 34 P - P 2 2 r r d amp A3 P 2 d P 1 b 5 S amp 7quot P amp A3 quot8 P 3 - 34 P C r x - 34 amp S c d P r quot S P i A quot A S P ii A P A A 3 A S amp B iii amp quot 0quot 6 x x t D y y t z z t S amp 2 2 2 S x y z ax by cz d 0 amp D S amp 7quot amp 2 2 2 1 2 3 0 4 x x t y y t z z t x y z ax by cz d amp amp amp 9 4 z y x t amp A3 4 S 7quot lt D B amp 2 lt 0 i S 7quot D amp 2 0 ii H S B D amp A3 H ampquot amp 2 gt 0 iii 2 1 7quot D t وt B وA 1 9 B وA quot S 2 1 3 2 1 t وt III o i j k D1 - x v y z x u y z y y x x x x u v i j k z z z z y y u 2 v u v 0 quot u 1 a 3 v u v 2 P P amp AB AC 0 amp E quot C B A b amp AB AC ABC amp 3 ABC amp 4 1 2 S AB AC S AB AD 3 ABCD F 4 amp 5 u amp A D 6 ampquot M AM u d M D u u v v u 7 u v u v u v u v w u v u w u v w u v v w S amp D 7quot amp 8 7quot gt d D

اوال ا ر ی وا I 1 F 1 f IR x x Log ln F1 0 ln 0 IR a ln D 0 f x u x ln b f x D u x gt f x u x ln f x D u x ln1 0 c e 271828 ln 1 e ln r r Q e r ln 2 r Q b gt 0 a gt 0 ln ln ln ab a b ln ln r a r a 1 ln ln a a ln ln ln a a b b ln ln a b a b ln ln a b a b lt lt ln ln ln ab a b ab gt 0 quot 0 quot a b ln ln ln gt a a b b 0 quot n ln ln a gt n a n a ln x 3 4 1 0 ln x x x gt ln u x u x u x ln u x u x u x quot 5 lim ln x x a ln lim ln x x b ln0 c ln lim 0 x x x d lim ln 0 x x x e ln1 lim 1 x x x 1 ln lim 1 x 1 x x ln ln 0 ln ln 0 1 t v x t u x v x v x t t w x t v x a t II 1 ln amp x x e a x R x e x gt x e R b 0 e 1 1 e e ln c x x e x R ln 0 x gt x e x 0 d x gt x y e y ln y x R 2 r Q x y R x y x y e e e x 1 x e e x x y y e e e rx x r e e x y e e x y x y e e x y lt lt 3 x x x e e R u x u x e u x e x ln x 0 1

quot 4 lim x x e a e lim 0 x x e b 0 e lim x x e c x lim 0 x x xe d 1 lim 1 x x e e x 1 t v x t t e v x t u x e x v x te w x e v x a t R a amp III 1 a 1 a amp R log a ln 0 log ln a x x x a gt 10 log log 10 ln 0 log log ln10 x gt x x x e amp - 2 log a ln amp log 1 a log 1 0 a a log1 0 log10 1 - - IV 1 ln 0 x x a gt a x a e 2 R y x b gt 0 a gt 0 x y x y a a a xy x y a a x x y y a a a x x x a b ab x 1 x a a x x x a a b b x y a a x y ln ln x a x a

ا ل I 1 card E E 2 amp n amp amp n n n 0 - amp n n 123 0 1 3 - amp2amp p 0 1 - amp 1 1 34 25 6 n 2 2 34 25 6 n np p 34 25 6 7amp28amp 9 3 ltamp gtamp 1 2 n n np quot 4 1 2 E a a a n p n A n E p amp 1 E n CD A p B a BD E GH A p B E F- 1 2 n x x x BD amp amp 7 amp 9 b p An amp 1 2 1 p n n facteurs n A n n n n p n p E n CD A n B F- E c 1 21 7I amp 9 d n A n n n n n E p amp JK 1 E n CD A p B JK e BD JK E GH A p LM F- 1 2 p x x x BD amp amp 7JKamp 9 f p Cn amp 1 2 1 1 21 p facteurs p p n n A n n n n n p C p p n p p p p amp 5 a 0 1 n C C n n 1 1 n C C n n n p n p C C n n 1 1 1 p p p C C C n n n ampNamp OAamp b n n k n k k n k a b C a b 2 E PampM1 A n E c n II 1 Qamp R 1 2 n 7Tamp - a a a A F- gtD amp Z6 amp V W Xamp 4 Y6 i D a 66X i 0 1 p i p 1 2 1 n p p p E i i Xamp ampP V p amp p a p 2 X A Xamp ampP V p b ltamp ampDTamp ampX8amp 7W Xamp a A Namp Y Xamp - amp 1 2 A a a a n 1 2 p A p a p a p a n Xamp ampP V p amp 3 A B CX B A a p A B p A p B p A B p A p B p A B CX B A b p A p A 1 A B amp Namp A X A c cd cd AJ ampX1 An A2 A1 d 1 2 1 2 n n p A A A p A p A p A 0 1 - 4 Y XTamp eJ 7T1 f g Xamp ampP V p Y XTamp eJ h ampDTamp ampX8amp fi 1 card X A card A p A card Y XTamp eJ ampDTamp ampX8amp f g - amp a 2quot nombredecas favorables p A nombredecas possibles kq rs 6gtD 1 j k D lamp m n 1 o 7W XTamp p b e D D amp o W 7amp-wquO rs 6 gt4 tuO rs - 7gtamp Y xD ampDTamp ampX8amp Y Xamp X W1 Ey quO D0amp z- amp c - amp amp Y xamp Oamp YX 1 2 n a a a 1 2 n p A p a p a p a eJ h Mamp 48amp tuO 6 1 4 amp M 3 34 Y Xamp G M 34 Y Xamp Y XTamp eJ h DJamp 48amp Y XTamp quot 3 B G 34 V YANampquot A Namp Y Xamp E X1 123456 45 ampDTamp ampX8amp Y Xamp E p p p x 2 4 6 2 p p p x 1 3 5 f p p p p p p 1 2 3 4 5 6 1 b x x x x x x 2 2 2 1 b 1 9 x 1 1 3 5 9 p p p 2 2 4 6 9 p p p A 36 1 2 1 3 6 9 9 3 p A p p 6 5 p A 0 CX B A

6 A Namp 1 B Namp Y X1 p A B p B A p A 7 8 9 6 p A 0 CX B A p A B p A p B A 9 7 ampX8amp Y6 a A1 A2 An - amp Z6 amp B i j i j A A 1 n i i A AJ z- amp Z6 amp B An A2 A1 ampX8amp b amp ampX8amp cd cd amp 7W XTamp O c A1 A2 An B X F B ampX1 1 1 n n p B p A p B A p A p B A quot lt 8 - amp Z6 amp I6 B A CNamp Y6 a p A B p A p B p B A p B - amp Z6 amp C6 B A Namp b 2amp V W X1 6 - amp b p A B p A cd cd 6 2amp n D R c p A p Xamp 2amp m 66 Y Xamp X A quot 2amp n YI2 Z D k k 6 A Nampquot Namp B 1 k k n k p B C p A p A n f Y Xamp X FM1 JAD 2quot F amp 2Tamp 1 amp E amp - amp a p Cn card A p A card 7amp 2amp k D0amp 9 J 7amp 2amp k D z- amp b BD F 76 gtamp 7 amp Y xamp E0 X amp amp 1 2 n X x x x i i 34 D0amp 0 x 6 9 8 III 66X D F- ZD X gt F- ampu rO 1 X BD X rOamp 2K ltamp 36 ampu rO X 2 1 2 X x x x n 4 amp X F Xamp 4 X 4 F6 i F p X x - YM m amp 9 l i n 12 n x 2 x 1 x i x n 1 2 i p X x 1 4gt 3 amp E X BD amp amp X ampu rO pamp F8amp 1 1 2 2 1 1 2 2 n n n n E X x p X x x p X x x p X x x x x 98 4 amp V X BD amp amp X ampu rO kOamp 2 2 X V X E X E X 2 2 2 1 1 2 2 2 2 1 1 2 2 n n n n n n E X x p X x x p X x x p X x x x x A B C 5 amp X BD amp amp X ampu rO ampgtamp ampTamp X V X DEF 6 amp F BD h ltamp ampamp X ampuamp rO 0amp amp lt x F X p X x x F F x 4 amp F ampamp X 4 Y6 Aamp R 3 3 4 B U N AAamp 7amp- 3 E FAamp P amp 7ampamp D x F- ZD amp ampuamp rOamp X X 9 8 GHampI J K a 3N V YANamp b X 0 1 2 B N V YANamp b X 1 2 1 B N V YANamp b X 2 3B V YANamp b X 3 X 01 23 X LM b 3 4 3 7 4 35 C p X C 1 2 3 4 3 7 18 1 35 C C p X C 2 1 3 4 3 7 12 2 35 C C p X C 3 3 3 7 1 3 35 C p X C 0 1 2 3 i x 1 35 18 35 18 35 4 35 i p X x c 4 4 18 1 49 0 1 2 3 35 35 35 35 35 E X d 2 2 2 2 2 4 4 18 1 75 0 1 2 3 35 35 35 35 35 E X 2 2 2 75 49 224 35 35 352 V X E X E X e 224 35 X V X x F F x E 0amp amp f F x p X x p 0 lt x 0 - amp 0 1 lt x - amp 4 35 F x p X x p X lt 1 2 lt x - amp 22 0 1 35 F x p X x p X p X lt 2 3 lt x - amp 34 0 1 2 35 F x p X x p X p X p X lt 3 lt x - amp F x p X x p X p X p X p X 0 1 2 3 1 lt

ا I تی I b و a و I ل دا f ت a f إ b اquotد اي b a f x dx واف ی b a f x dx F b F a F دا أص quotا f b b a a f x dx F x F b F a ی تی ا- 2 xي - 01 b b a a f x dx f t dt II خ ت I c و b و a و I ل دا g و f 0 1 a a f x dx 2 a b b a f x dx f x dx 3 b c b a a c f x dx f x dx f x dx ل4 56 4 b b b a a a f x g x dx f x dx g x dx 5 b b a a af x dx a f x dx a IR 6 اquotا x a F x f x dx ه اquotا ا8ص quotا f ا تgtquotم a 0 x a b f x و a b نآ إذا a 7 ن 0 b a f x dx 0 x a b f x و a b نآ إذا b ن 0 b a f x dx x a b f x g x و a b نآ إذا c ن b b a a f x dx g x dx d إذا آن a b و ن b b a a f x dx f x dx دquotا a 8 1 b a f x dx b a ی اC اسA quotا f b و a F b و a ر F c دquot quotجی b b a f x dx b a f c c 1 b a m f x dx M b a Cا Gه M و m اquotی واC اC ی quotا a b f اHص 8 تت a و GI J b III تت quotب ا 1 ا ampاء و f نت F I ل قC4L 5 دا g و f ltیquot I b و a و I g b b b a a a f x g x dx f x g x f x g x dx IV ول اوال ا ا-دی f F 0 1 a 0 ax 1 r x r 1 1 1 r x r 1 r u u r 1 1 1 r u r 2 1 x 1 x u u 1 u 1 x 2 x u u 2 u 1 x ln x u u ln u x e x e ax e 1 ax e a f F u x u e u x e 2 1 1 x arctan x 2 1 u x u x arctan u x cos x sin x sin x cos x 2 2 1 tan 1 cos x x tan x cos ax b 1 sin ax b a sin ax b 1 cos ax b a 2 2 1 tan 1 cos ax b ax b 1 tan ax b a u x u x cos sin u x u x u x sin cos u x 2 u x u x 1 tan tan u x

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