Basic differentiation and integration formulas

Basic differentiation and integration formulas -...

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Unformatted text preview: Differentiation Formulas Integration Formulas d k=0 dx d [f (x) ± g (x)] = f (x) ± g (x) dx d [k · f (x)] = k · f (x) dx d [f (x)g (x)] = f (x)g (x) + g (x)f (x) dx g (x)f (x) − f (x)g (x) d f (x) = 2 dx g (x) [g (x)] d f (g (x)) = f (g (x)) · g (x) dx dn x = nxn−1 dx d sin x = cos x dx d cos x = − sin x dx d tan x = sec2 x dx d cot x = − csc2 x dx d sec x = sec x tan x dx d csc x = − csc x cot x dx dx e = ex dx dx a = ax ln a dx 1 d ln |x| = dx x d 1 sin−1 x = √ dx 1 − x2 d −1 cos−1 x = √ dx 1 − x2 d 1 tan−1 x = 2 dx x +1 d −1 cot−1 x = 2 dx x +1 d 1 √ sec−1 x = dx |x| x2 − 1 d −1 √ csc−1 x = dx |x| x2 − 1 (1) (2) (3) (4) dx = x + C xn dx = xn+1 +C n+1 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) dx = ln |x| + C x ex dx = ex + C (5) ax dx = (6) (7) (8) (9) (10) tan x dx = − ln | cos x| + C (11) cot x dx = ln | sin x| + C (12) (13) (14) (15) (16) csc2 x dx = − cot x + C (17) sec x tan x dx = sec x + C (18) csc x cot x dx = − csc x + C (19) (20) (21) (22) √ x dx = sin−1 + C a a2 − x2 (17) (16) (15) (14) sec x dx = ln | sec x + tan x| + C 1x a +C ln a ln x dx = x ln x − x + C sin x dx = − cos x + C cos x dx = sin x + C csc x dx = − ln | csc x + cot x| + C (12) sec2 x dx = tan x + C (13) dx 1 x = tan−1 + C a2 + x2 a a dx 1 |x| √ = sec−1 +C 2 − a2 a a xx (18) (19) ...
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This note was uploaded on 04/11/2011 for the course MECH 294 taught by Professor Mr.wang during the Spring '11 term at Hong Kong Polytechnic University.

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