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Calculus II                                                          Quiz #1                                             February 17, 2004

Name____________________                   R.  Hammack                                                 Score ______
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Find the following antiderivatives.

(a)  ∫ (x^5 + 2x^2 - 1)/x^4dx = ∫ (x^5 /x^4 + (2x^2)/x^4 - ( 1)/x^4) dx = ∫ (x + 2/x^2 - ( 1)/x^4) dx =

∫ (x + 2x^(-2) - x^(-4)) dx = x^2/2 + 2x^(-1)/-1 - x^(-3)/-3 + C = x^2/2 - 2/x + 1/(3x^3) + C



(b)  ∫ ( 2/x + e^x ) dx = 2ln | x | +e^x + C



(c) ∫e^x^22x dx =∫e^u du = e^u + C = e^x^2 + C

u = x^2
du = 2x dx



(d)   ∫x/(4x^2 + 4)^3dx = 1/8∫ (8x)/(4x^2 + 4)^3dx = 1/8∫1/u^3du = 1/8 -1/(2u^2) + C = -1/(16 (4x^2 + 4)^2) + C

u = 4x^2 + 4  du = 8x dx



(e) ∫e^x/(1 +   e^(2x)) dx = ∫e^x/(1 +    ( e^x)^2) dx = ∫1/(1 +   u^2) du = tan^(-1)(u) + C = tan^(-1)(e^x) + C

u = e^x  du = e^x dx