Ap BC Calculus Unit 6

∫ (sec x tan x)dx = ?

(sec x) + C

∫ sinx dx

-cosx + c

∫ csc^2 x dx =

-cot x + C

∫ csc x + cot x dx=

-csc x + C

∫ 0 dx

C

∫ kf(x) dx

k ∫ f(x) dx

∫ k dx

kx + C

∫ cos x dx=

sin x + C

∫ sec^2(x) dx

tanx + C

∫ x^n dx

x^(n+1)/(n+1) + C

The Integral of 1/x

∫ 1/x = ln | x | + C

Integration for Bases Other Than e

∫ aˣ dx=(aˣ/lna) + C

The Integral of the Natural Logarithmic Function

∫ eˣ dx = eˣ + C

∫ [f(x) + g(x)] dx

∫ f(x) dx + ∫ g(x) dx

∫ f(x) - g(x) dx

∫ f(x) dx - ∫ g(x) dx

The Fundamental Theorem of Calculus

∫^b f(x) dx = F(b) - F(a) , where F is any antiderivative of f, that is, F prime= f