Table of Integrals: Basic Forms, Integrals With Roots, Rational Functions

Table of Integrals BASIC FORMS INTEGRALS WITH ROOTS (1) fxxdx= (18) [vx-adx==(x-a)^ (2) f-dx=1nx (19) (3) Sudv=uv-[vdu (20) (4) (21) RATIONAL FUNCTIONS (22) (5) (23) = (6) (24) (7) n - 1 (25) (8) (9) State (26) (10) (27) (11) (28) (12) 4a3/2 (13) = (29) (14) B'In(2Vavx+2vb+ar) 8a5/2 (15) (30) x+xa (16) (31) 2a (17) (32) [ (33) /

(34) (49) [ (35) (50) (36) STATE EXPONENTIALS (37) (51) Se"dx=1e (38) (52) erf(ivax) where (39) (53) fxx`dx=(x-1)e (54) (55) [x e'dx=e'(x2-2x+2) (40) (56) (57) (41) (58) where / (42) (59) LOGARITHMS (43) TRIGONOMETRIC FUNCTIONS (44) (60) sin xdx = - cos x (45) (61) [sin' xdx= (62) (46) (63) cosxdx = sinx = (47) (64) (65) (48) (66) =

(67) Sx" cosaxdx (89) (68) (90) [.xsin.xdx=-xcos.x+sin.u (69) (91) (70) tanxxxx-incos.x (92) xsinxdx=(2-x2)cosx+2xsinx (71) (72) (73) [sec.xdx=lnlsec.x+tan. TRIGONOMETRIC FUNCTIONS WITH eax (74) sec2 xdx = tanx (95) (75) (76) sec.xtan.xdx=sec.x (97) (77) (78) (98)(axax (79) fcsc.ddr=Inlcscx-cotxi TRIGONOMETRIC FUNCTIONS WITH x" AND eax (80) [csc2 xdx = - cot.x (99) (100) Sex (82) HYPERBOLIC FUNCTIONS (83) [sec.xcsc.xdx: Intan.x (101) cosh xdx = sinh x TRIGONOMETRIC FUNCTIONS WITH x" (102) Sear (84) (103) sinh xdx = cosh x (85) (86) xcosxdx 2xcosx+(x2-2)sinx (105) (87) (106) [tanhandr==Incoshar Sx" cos xdx = (88) [cosaxcoshbxdx= (107) [asin axcosh bx + bcosaxsinhbx

Scos ax sinh bxdx = (108) atbal 1 [bcos bx ax cosh bx + asin ax sinh ] sin ax cosh bxdx = (109) 1 - a cos ax cosh bx + bsin ax sinh bx 1 S sin ax sinh bxdx = (110) 1 g'+bz[bcosh bxsin ax - acos ax sinh bx] (111) sinh ax cosh axdx = 1/4 [-2ax + sinh(2ax)] sinh ax cosh bxdx = (112) bi-a2 1 [b cosh bx sinh ax - a cosh ax sinh bx ]