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Differentiation Formulas, Integration Formulas, d, k = 0, dx, (1), dx = x + C, (1), d, [f(x) ± g(x)] = f'(x) ± g'(x), dx, rn+1, + C, n +1, (2), x" dx, (2), d., [k f(x)] = k - f' (x), (3), dx, = In |a| + C, dx, (3), d, [f(x)g(x)] = f(x)g'(x) + g(x)f (x) (4), g(x)f"(x) – f(x)g'(x), d.x, e* dx = e* +C, (4), f(x), g(x), d, (5), dx, 1, -a" +C, In a, d, at d.x =, (5), de (g(x)) = f'(g(x)) · g'(x), (6), d, In x dx = x ln x – x + C, (6), nx"-1, (7), dx, d., sin x = cOS x, dx, (8), sin x d.x = - cos x + C, (7), d, Cos x = - sin r, d.x, (9), cos x dx = sin x + C, (8), d, tan x = sec x, d.x, (10), tan x dx = - In cos x|+ C, (9), d., cot x = - csc?, dx, (11), cot x dx = In| sin x| +C, (10), d, sec x = sec x tan x, d.r, (12), d, CSC x =, dx, (13), sec x dx = ln sec x + tan x+ C, (11), csc x cot x, d, et = e", dx, (14), csc x dx = - In csc x + cot r+C (12), d, a" = a" In a, dx, (15), sec? x dx = tan x + C, (13), d., 1, In r|, dx, (16), csc x dx = - cot x + C, (14), 1, 1, sin, dx, (17), = x, sec x tan x dx = sec x + C, (15), d, -1, -1, COS, (18), dx, /1, csc x cot x d.x = - csc x + C, (16), d, tan, d.x, (19), x2 + 1, d.x, d, -1, cot, = sin-1 x, + C, -1, (17), (20), Va? – x2, d.x, x2 +1, d., sec, dx, 1, d.x, (21), 1, tan, -1, +C, (18), a2 + x?, a, a, d, -1, |x|, + C, d.x, 1, CsC, dx, (22), -1, sec, (19), %3D, xvx2 – a², a, a