微积分公式（Calculus formula）.doc

微积分公式（Calculus formula） 微积分公式 Sin x = cos x DX Cos x = - sin X Sec2 as x = x Csc2 X - X = COT SEC x = sec x as X CSC x = - CSC x Cot X Dx = - sin x cos x + C Cos x DX = sin X + C So X, dx = ln sec x + C | | Cot X, dx = ln x + C | without | SEC X, dx = ln sec x + | | as X + C CSC X, dx = ln | CSC x Cot x + C - | No - 1 (- X) = - X - 1 Cos (x 1 - X - 1) = - cos So - (1 - X) = - X - 1 COT (x 1 - X - 1) = - Cot SEC 1 SEC (- X) = - X - 1 CSC - (x 1 - X - 1) = - CSC Dx = - 1 (no) (1) = - cos So (= - 1) COT (= - 1) Sec = (- 1) CSC - 1 = (X / a) No - 1 x DX = X sin X - 1 + C Cos x cos x DX = - 1 - 1 - X + C So - So - DX = x 1 x 1 x - ln (1 + x2 + c) Toc toc dx = x 1 - X - x 1 + ln (1 + x2 + c) SEC X, dx = X - 1 - 1 - LN sec x + X + C | | CSC - 1 x DX = 1 + ln X - X CSC | | + X + C Sinh (- 1) = ln (X +) XR COSH (- 1) = ln (X +) x≥1 TANH (- 1) = ln (X) | | 1 Sech (- 1) = ln (+) 0≤x≤1 Csch (-) = ln (1 + X) | | 0 COSH x = Sinh x DX COSH x = Sinh X TANH (x = x sech2 - csch2 COTH x = x Sech Tanh Sech x = X - X Csch csch COTH x = X - 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 = - 1 (2Tan - e - X) + C Csch dx = ln x 2 + C | | DUV = UDV + VDU DUV UV = UDV = + VDU The UDV = UV VDU Cos2θ - sin2θ = cos2 Cos2θ + sin2θ = Cosh2θ - sinh2θ = Cosh2θ + sinh2θ = cosh2 Sinh (DX) = - 1 COSH (= - 1) TANH (= - 1) COTH (= - 1) Sech (= - 1) Csch - 1 = (X / a) Sinh X, dx = - 1 - 1 - X Sinh x + C COSH x DX = - 1 - 1 - X COSH x + C Tanh - 1 x DX = 1 + ln X - X Tanh | x2 + C 1 - | COTH X, dx = X - 1 - 1 - LN | COTH x 1 - | x2 + C Sech Sech x x DX = - 1 - 1 - 1 x - X + C Csch - 1 x DX = x csch - 1 x + Sinh x + C - 1 Without 3θ = 3sinθ - 4sin3 Cos3θ = 4cos3θ - 3cos →sin3θ = (3sinθ - sin3 →cos3θ = (3cosθ + cos3 Sin x cos x = = Sinh x = COSH x = 正弦定理: = = = 2R 余弦定理: A2 = B2 + C2 2bc cos A2 = B2 + C2 css11506-2ac cos C2 = A2 + B2 - 2AB cos Without (α±β) = cos Alpha cos alpha + beta without without Cos (α±β) = cos Alpha cos Alpha B