Standard Differentials and Integrals
Equations for differentials and integrals.
Differentials
(d/dx) xn = n xn-1 (1)
(d/dx) ln x = 1 / x (2)
(d/dx) eax = a eax (3)
(d/dx) ax = ax ln a (4)
(d/dx) xx = xx(1 + ln x) (5)
(d/dx) sin x = cos x (6)
(d/dx) cos x = - sin x (7)
(d/dx) tanx = sec2 x (8)
(d/dx) cot x = - cosec2 x (9)
(d/dx) sin-1x = 1 / (1 - x2)1/2 (10)
(d/dx) cos-1x = -1 / (1 - x2)1/2 (11)
(d/dx) tan-1x = 1 / (1 + x2) (12)
(d/dx) cot-1x = -1 / (1 + x2) (13)
Integrals
∫ xn dx = xn+1 / (n + 1) n ≠ - 1 (14)
∫ 1 / x dx = ln x (15)
∫ eax dx = eax / a a ≠ 0 (16)
∫ ax dx = ax / ln a a > 0, a ≠ 1 (17)
∫ ln x dx = x (ln x - 1) (18)
∫ sin x dx = - cos x (19)
∫ cos x dx = sin x (20)
∫ tan x dx = - ln(cos x) (21)
∫ cot x dx = ln(sin x) (22)
∫ sec2 x dx = tan x (23)
∫ cosec2 x dx = - cot x (24)
∫ 1 / (1 - x2)1/2 dx = sin-1 x |x| < 1 (25)
∫ 1 / (1 + x2) dx = tan-1 x |x| < 1 (26)
