MATH 201 Useful File Integral, Spring 2016

l pT: j i ntegrals with Trigonometric Functions . : 3cosar cos3ar } é aie sin ardz —_— + —— (66 s Integrals of Hyperbolic Functions | sa = —sinaz (67) e [« sh ard. = sinh « ns Pog 1 1 a (68) ese’ adr = 5 cot reser + 5 In csezr — cotz (90) = i) fe cosh brdr 1 Lie esc” r cot rdz = esc"7,.n #0 (91) — |a cosh bz bsint ox xb r ] p l+p13+p 4 ) [= 1 In| tan (92) r aFi | > pe (69) i z Products of Trigonometric Functions and 4 eee, Sian (70) aaa Misaainlals [ sinh axe = cosh as eo. ae 12a . . ‘ cosi(a—b)z] _ cosi(a+b)z] 1, er ae (93) fe" sinh bade = [= az sin brdz = 2(a —) 2(a +h) (7) 1 i <—_|=bcoshbe+-nsinhhe] a¥b [ sesands = — cosur + — sinaz (94) 1 Ps a é z es = (2a — b)z] oe yee 4a 2 [ so? azcovteds . [2 coszaz = 2xcosz + (x* — 2)sinz (95) sin|(2a + b)z wre == — a : “* tanh brdr = : S omands = OE OE nae (06) is. i a? rr ¢ F, el a vs FET [ a? scossd =3sin's (73) (a4) J q ee ! ek: Cs Lakes a gad P(n + 1,-12 ue = cos|(2a — b)z] _ cosbr [= eet a , eo — 2tan"[e"*] ng [- arsinbrdt = 4g 6) 2b +(-1)"P(n + 1,27) (97) a (2a + b) 74) 1 - ae (74) J tanhazde = = Incoshaz 115 sy a JF cosaxde = Flia)!-" (1) (n+ 1, ~taz) . =—-> cos ar " [one mee -P(n + 1, iza) (98) J cosareost brdr = > jasin.az cosh hr Be eee weltia el +bcos ax sinh br (1 dntazcom baedr=4~ “yg (16(a : b) [rs adr = —rcosr+sinz (99) sin he _ sinf2(a+b)z] (76) ; +e 16(a +b) [ esinaxde = (100) J cosazsinh beds = = ——— [bcos ax cosh br a a +P ; x sindaz 77 asin az sinh be (117) sin’ ar cos’ ard = 5 - —35, 7 J #sinzae - (2-—2*) cosz + 2xsinz (101) 1 78) axdz = —— \Incosar { [m= a [ow az cosh brdz = —!__ Fz |-acos.ax cosh bz 1 2-a'r? 2zr sin ax —— jw? axas = -r+~tanaz (79) J #snazde Se oeeR te (i0R) bsin az sinh bz} (118) - oe Bie ade Ss ci " f= azds = Tn) # sin ade = —5(i)" [P(n + 1, -iz) — (~1)"P(n + 1, -iz)] [vax sinh beds Gz [boosh br sin ax— e+e +4 (103 fi (*F i,> 3 ~ tan az) (80) ) aeons az sinh hr} (119) Products of Trigonometric Functions and Jin? axe Bee . poet az (81) Exponentials a [ sitaz cust ards = — [-Qax + sinh 2ew (120) da 1 sei z e = -¢7 (si i idl am tn | cc + toma i (tan =) (82) fe sin gdr = 3° (sin x — cos x) (104) J sna cosh bd = Grr (boosh br sinh a ‘ as ic ? coe : tan as (a) [e sin ade = ——Se™(bsin ur —avosax) (105) ~a cosh az sinh ba (121) eg) ewes AE re maitabitity of the reat ti | von, viet http /ferent i recommen ry i