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Section5_4_review - Section 5.4 Indefinite Integrals f xs...

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Section 5.4: Indefinite Integrals The indefinite integral is fx ( 29 dx = Fx ( 29 , where F x ( 29 = fx ( 29 so F x ( 29 is the most general antiderivative of f x ( 29 . An indefinite integral represents a family of functions. An indefinite integral is assumed to be valid on an interval so discontinuities associated with the integrand f x ( 29 are not an issue. Table of Indefinite Integrals(where a , c , and k are constants) a fx ( 29 dx = afx ( 29 dx fx ( 29 + gx ( 29 [ ] dx = fx ( 29 dx + gx ( 29 dx kxdx = kx + c x n dx = x n + 1 n + 1 + c , n ≠- 1 sin xdx =- cos x + c cos xdx = sin x + c sec 2 xdx = tan x + c csc 2 xdx =- co t x + c sec x tan xdx = sec x + c csc x co t xdx =- csc x + c Example. Evaluate 3cos φ + φ ( 29 d φ . Solution. 3cos φ + φ ( 29 d φ = 3sin φ + φ 2 2 + c Example. Evaluate sec θ tan θ d θ . Solution. sec θ tan θ d θ = sec θ + c Example. Evaluate x 1 + 2 x 4 ( 29 dx . Solution. x 1 + 2 x 4 ( 29 dx = x + 2 x 5 ( 29 dx = x 2 2 + 2 x 6 6 + c = x 2 2 + x 5 3 + c Example. Evaluate sin2 x sin
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