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58x The partial fraction decomposition of f (ac) 8x2 - 10x + 3 can be written in the form of g (2 ) + 2x - 1 4x - 3 where f (ac) = g(a) =48 its) 9(w) can be written in the form of + :82 _ 4 a: 2 a: + 2 The partial fraction decomposition of , where M) = :1 ' .90\") = :1 The partial fraction decomposition of ac2 + 23 f(a) g x) 23 + 2-2 can be written in the form of h(ac) + + x+1' where f (ac) = g(2) = h (ac) =85 The velocity of a particle moving along a line is a function of time given by \"(t) = . Find t2 + 15t + 54 the distance that the particle has traveled after t = 4 seconds if it started at t = 0 seconds. [:1 3:1: + 22 Consider the indefinite integral d3: :1: + 6 a m+6 Using long division to rewrite the integrand we can write the integral in the form [k + do: where k = C] a=l:] Integrating term by term, we obtain 3+6 Use absolute value bars if necessary, but do not nest absolute value bars inside parenthese. 3 2 :1: 5a: 16:1: 20 Consider the indefinite integral /H24 do: w _ Then the integrand decomposes into the form [Note: Your first step will be long division] d as: + b + + a: 2 a: + 2 Integrating term by term, we obtain that jm3+5m2 16:620 dm= 51:24 0