Antiderivatives Suppose F and G are antiderivatives of f and g, respectively, so that F f and G g. Function Antiderivative Reason cf x cF x d dx cF x d dx F x f x g x F x G x xn 1 n 1 d dx 1 x ln x d dx ln x ex ex d dx ex ax ax ln a d dx x n (n 1) MAT 111: Calculus I cf x G x xn 1 n 1 ax ln a x n (n f x 1) 1 x ex ax Chapter 4: Applications of Differentiation g x More Antiderivatives Function Antiderivative Reason cos x sin x d dx sin x sec2 x csc x cot x sec x tan x csc2 x 1 1 x2 1 1 x2 1 1 x2 cos x d dx d dx tan x csc x d dx d dx sec x cot x d dx sin 1 x d dx cos 1x tan 1x MAT 111: Calculus I sin x cos x cos x sin x sec2 x tan x csc x sec x csc x cot x sec x tan x cot x csc2 x sin 1 1 d dx cos 1x d dx tan 1x x 1 x2 1 1 x2 1 1 x2 Chapter 4: Applications of Differentiation
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