Standard 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) tan(x) = sec2(x) (8)
(d/dx) cot(x) = - cosec2(x) (9)
(d/dx) sin-1(x) = 1 / (1 - x2)1/2 (10)
(d/dx) cos-1(x) = -1 / (1 - x2)1/2 (11)
(d/dx) tan-1(x) = 1 / (1 + x2) (12)
(d/dx) cot-1(x) = -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)
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