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Integral Calculus Formula Sheet

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Integral Calculus Formula Sheet


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Description

Formulas from Calculus Derivatives [ex ]

1 √ 2 x

1 x ln b

[f (x)g(x)] = f 0 (x)g(x) + f (x)g 0 (x)

Product Rule:

Quotient Rule:

d f (x) g(x)f 0 (x) − f (x)g 0 (x) = dx g(x) g(x)2

Chain Rule:

d [f (g(x))] = f 0 (g(x))g 0 (x) dx

Special Cases d'[f (x)n ] dx d'1 dx g(x) 

d [ln |f (x)|] = dx d'h f (x) i e dx

−g 0 (x) g(x)2 f 0 (x) f (x)

Integrals Z

f (u) du = F (u) + C = F (g(x)) + C Z g(b)

f 0 (x) dx = ln |f (x)| + C f (x)

ef (x) f 0 (x) dx = ef (x) + C

By parts

f (x)g (x)dx = f (x)g(x) − 0

1 x ln b b

Special cases

Substitution