Dx sin x=cos x cos x = -sin x tan x = sec2 x cot x = -csc2 x sec x = sec x tan x csc x = -csc x cot x sin x dx = -cos x + C cos x dx = sin x + C tan x dx = ln |sec x | + C cot x dx = ln |sin x | + C sec x dx = ln |sec x + tan x | + C csc x dx = ln |csc x – cot x | + Csin-1(-x) = -sin-1 xcos-1(-x) = - cos-1 xtan-1(-x) = -tan-1 xcot-1(-x) = - cot-1 xsec-1(-x) = - sec-1 xcsc-1(-x) = - csc-1 xDx sin-1 (ax )=221ax cos-1 (ax )=221axtan-1 (ax )=22aaxcot-1 (ax )=22aaxsec-1 (ax )=22axxacsc-1 (ax )=22axxa sin-1 x dx = x sin-1 x+21x+C cos-1 x dx = x cos-1 x-21x+C tan-1 x dx = x tan-1 x- ?ln (1+x2)+C cot-1 x dx = x cot-1 x+?ln (1+x2)+C sec-1 x dx = x sec-1 x- ln |x+12x|+C csc-1 x dx = x csc-1 x+ ln |x+12x|+Csinh-1 (ax )= ln (x+22xa) xRcosh-1 (ax )=ln (x+22ax) x ≧1tanh-1 (ax )=a21 ln (xaxa) |x| <1coth-1 (ax )=a21 ln (axax) |x| >1sech-1(ax )=ln(x1 +221xx)0 ≦x≦1csch-1 (ax )=ln(x1 +221xx) |x| >0Dx sinh x = cosh x cosh x = sinh x tanh x = sech2 x coth x = -csch2 x sech x = -sech x tanh x csch x = -csch x coth x sinh x dx = cosh x + C cosh x dx = sinh x + C tanh x dx = ln | cosh x |+ C coth x dx = ln | sinh x | + C sech x dx = -2tan-1 ( e-x) + C csch x dx = 2 ln |xxee211| + Cduv = udv + vdu d uv = uv = udv + vdu→udv = uv - vducos2θ -sin2θ =cos2θcos2θ + sin2θ =1cosh2θ -sinh2θ =1cosh2θ +sinh2θ =cosh2θDx sinh-1(ax )= 221xacosh-1(ax )= 221axtanh-1(ax )= 22aaxcoth-1(ax )=22aaxsech-1(ax )= 22xaxacsch-1(ax )=22xaxa sinh-1 x dx = x sinh-1 x-21x+ C cosh-1 x dx = x cosh-1 x-12x+ C tanh-1 x dx = x tanh-1 x+ ? ln | 1-x2|+ C coth-1 x dx = x coth-1 x- ? ln | 1-x2|+ C sech-1 x dx = x sech-1 x- sin-1 x +...
