# formulas - (for all x) Hyperbolic sinh x dx = cosh x + C...

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Power of x. x n dx = x (n+1) / (n+1) + C (n -1) Proof 1/x dx = ln|x| + C Exponential / Logarithmic e x dx = e x + C Proof b x dx = b x / ln(b) + C Proof , Tip! ln(x) dx = x ln(x) - x + C Proof Trigonometric sin x dx = -cos x + C Proof csc x dx = - ln|CSC x + cot x| + C Proof COs x dx = sin x + C Proof sec x dx = ln|sec x + tan x| + C Proof tan x dx = -ln|COs x| + C Proof cot x dx = ln|sin x| + C Proof Trigonometric Result COs x dx = sin x + C Proof CSC x cot x dx = - CSC x + C Proof sin x dx = COs x + C Proof sec x tan x dx = sec x + C Proof sec 2 x dx = tan x + C Proof csc 2 x dx = - cot x + C Proof Inverse Trigonometric arcsin x dx = x arcsin x + (1-x 2 ) + C

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arccsc x dx = x arccos x - (1-x 2 ) + C arctan x dx = x arctan x - (1/2) ln(1+x 2 ) + C Inverse Trigonometric Result
dx ( 1 - x 2 ) = ar cs in x + C dx x ( x 2 - 1) = ar cs ec| x| + C dx 1 + x 2 = ar ct an x + C Useful Identities arccos x = /2 - arcsin x (-1 <= x <= 1) arccsc x = /2 - arcsec x (|x| >= 1) arccot x = /2 - arctan x

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Unformatted text preview: (for all x) Hyperbolic sinh x dx = cosh x + C Proof csch x dx = ln |tanh(x/2)| + C Proof cosh x dx = sinh x + C Proof sech x dx = arctan (sinh x) + C tanh x dx = ln (cosh x) + C Proof coth x dx = ln |sinh x| + C Proof Power of x. c = 0 x = 1 x n = n x (n-1) Proof Exponential / Logarithmic e x = e x Proof b x = b x ln(b) Proof ln(x) = 1/x Proof Trigonometric sin x = cos x Proof csc x = -csc x cot x Proof cos x = - sin x Proof sec x = sec x tan x Proof tan x = sec 2 x Proof cot x = - csc 2 x Proof Inverse Trigonometric arcsin x = 1 (1 - x 2 ) arccsc x = -1 |x| (x 2- 1) arccos x = -1 (1 - x 2 ) arcsec x = 1 |x| (x 2- 1) arctan x = 1 1 + x 2 arccot x = -1 1 + x 2 Hyperbolic sinh x = cosh x Proof csch x = - coth x csch x Proof cosh x = sinh x Proof sech x = - tanh x sech x Proof tanh x = 1 - tanh 2 x Proof coth x = 1 - coth 2 x Proof...
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## This note was uploaded on 05/19/2011 for the course PHYSICS 10 taught by Professor Darp during the Spring '11 term at Mapúa Institute of Technology.

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formulas - (for all x) Hyperbolic sinh x dx = cosh x + C...

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