FOrumla sheet study guide - MA103 Final Examination Page 1 of 1 Antiderivatives Trigonometric Identities Z f(u du denotes the general antiderivative of

# FOrumla sheet study guide - MA103 Final Examination Page 1...

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MA103 - Final Examination Page 1 of 1 Antiderivatives Z f ( u ) d u denotes the general antiderivative of f ( u ). If Z f ( u ) d u = F ( u ) + c then d F ( u ) d u = f ( u ). Z u n d u = u n +1 n + 1 + c , n 6 = 1 Z 1 u d u = ln | u | + c Z e u d u = e u + c Z a u d u = a u ln a + c , 1 6 = a > 0 Z sin u d u = cos u + c Z cos u d u = sin u + c Z sec 2 u d u = tan u + c Z csc 2 u d u = cot u + c Z sec u tan u d u = sec u + c Z csc u cot u d u = csc u + c Z tan u d u = ln | sec u | + c Z cot u d u = ln | sin u | + c Z sec u d u = ln | sec u + tan u | + c Z csc u d u = ln | csc u + cot u | + c Z sinh u d u = cosh u + c Z cosh u d u = sinh u + c Z sech 2 ( u )d u = tanh( u ) + c Z d u a 2 u 2 = sin 1 u a + c , a > 0 Z d u u u 2 a 2 = 1 a sec 1 u a + c , a > 0 Z d u u 2 + a 2 = 1 a tan 1 u a + c Z d u u 2 + a 2 = 1 a cot 1 u a + c Trigonometric Identities sin 2 x + cos 2 x = 1 sec 2 x tan 2 x = 1 csc 2 x cot 2 x = 1 sin( x + y ) = sin x cos y + cos x sin y cos( x + y ) = cos x cos y sin x sin y tan( x + y ) = tan x + tan y 1 tan x tan y sin 2 x = 2 sin x cos x cos 2 x = 1 2 sin 2 x = 2 cos 2 x 1 sin 2 x = 1 2 (1 cos 2 x ) cos 2 x = 1 2 (1 + cos 2 x ) tan 2 x = 2 tan x 1 tan 2 x Derivatives of Inverse Trigonometric Functions d dx sin 1 x = 1 1 x 2 d dx cos 1 x = 1 1 x 2 d dx tan