Antiderivative Rules - List, Formulas, Examples | What are ...
These antiderivative rules help us to find the antiderivative of sum or difference of functions, product and quotient of functions, scalar multiple of a function and constant function, and composition of functions.
2 Antiderivatives Rules If the antiderivative of f(x) is F(x), and the antiderivative of g(x) is G(x) then The antiderivative of af(x)+bg(x) is aF(x)+bG(x) (for any a, b) The antiderivative of f(ax+b) is 1 a F(ax+b) As a result: If f(x) = (dx+b)a then F(x) = 1 d (dx+b)a+1 a+1 +C (unless a = 1) If f(x) = 1 ax+b then F(x) = 1 a ln(ax+b)+C If f(x ...
BASIC ANTIDERIVATIVE FORMULAS YOU REALLY NEED TO KNOW !! ex dx = ex +C ax dx = ax lna +C 1 x dx =ln|x| +C cosxdx=sinx+C sec2 xdx=tanx+C sinxdx= −cosx+ C csc2 xdx= −cotx +C secxtanxdx=secx+ C 1 1+x2 dx =arctanx+C 1 √ 1− x2 dx =arcsinx+C cscxcotxdx= −cscx+ C secxdx=ln|secx+tanx|+ C cscxdx= −ln|cscx+cotx|+ C xn dx = xn+1 n+1 +C, when n = −1 Here …
Table of antidifferentiation formulas Function Particular antiderivative Function Particular antiderivative xn(n 6= 1) xn+1 n+1 1 x lnjxj ex ex ax(a > 0) ax ln a cos x sin x sin x cos x sec2 x tan x sec xtan x sec x 1 1+ x2 tan 1 x 1 p x2 sin 1 x cosh x sinh x sinh x cosh x csc2 x cot x csc xcot x csc x Let f and gbe two functions defined on ...
4.9: LIST OF GENERAL ANTIDERIVATIVES FUNCTION ANTIDERIVATIVE f(x) = xn (n 6= −1) F(x) = 1 n+1 xn+1 +C f(x) = x−1 = 1 x F(x) = ln|x|+ C f(x) = ex F(x) = ex + C f(x ...
AP Calculus Formula List Math by Mr. Mueller Page 3 of 6 ( ) ( ) ( )( ) 1 1 Derivative of an Inverse Function: ' 1 ' f x f f x − − = _____ ( ) ( ) ( ) a First Fundamental Theorem of Calculus: ' b ∫ f x dx f b f a= −
Antiderivatives Definition 1 (Antiderivative). If F0(x) = f(x) we call F an antideriv-ative of f. Definition 2R (Indefinite Integral). If F is an antiderivative of f, then f(x)dx = F(x) + c is called the (general) Indefinite Integral of f, where c is an arbitrary constant. The indefinite integral of a function represents every possible ...
ANTIDERIVATIVES: RULES, FORMULAS, ETC. Definition: An antiderivative of a function f(x) is a function F(x) for which F0(x) = f(x). Note: The Mean Value Theorem states that all antiderivatives of a given function differ at most by a constant. Thus if F is an antiderivative of f, any antiderivative of f must be of the form F(x)+C, where C is a ...
Two antiderivatives differ by constant. If F is any antiderivative of f, then every antiderivative of f is of the form F(x) + C for some constant C. Here is the veri cation: Let F be an antiderivative of f and suppose that G is another antiderivative of f. We have F 0(x) = f(x) and also G 0(x) = f(x), so that F (x) = G (x). Let H(x) = G(x) F(x).
Table of antiderivatives I skip +Cin the right-hand expression Powers and logarithms xa 8 <: 1 a+1 xa+1 a6= 1 logjxj a= 1 x logx ( +1+1) 1x+1 logx ( +1) 2x Exponents e xe ax (loga) 1ax xex (x 1)ex e xe Trigonometric functions cosx sinx sinx cosx tanx logjcosxj cotx logjsinxj sec2 x tanx csc2 x cotx Hyperbolic functions coshx sinhx