Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F(x) and G(x) are antiderivatives of f (x) and g(2) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, of (ac) dac = CF (x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, / [f (20) + 9 (x) ] dxc = F(x) + G(2) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, if(:) - g(x)] dac = F() - G(x) + C. artl The power rule: / x dx = rtitC,r # -1. NOTE: Enter the exact answer. 6 By + dy +Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. tv 4t2 + 5 dt = +CEvaluate the integral / (3 + sint) cost at using the substitution u = 3 + sint. (3 + sint) cost dt = +CEvaluate the integral cos () sin(x) dx using the substitution u = cos(x). cos"(x ) sin(x) da = CEvaluate the integral f 2x(x2 + 3)1 do using the substitution 2 = x2 + 3. 2at (3 2 + 3) 11 dx = +C\fEvaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. +C(a) Evaluate the integral using the substitution x In(62) u = In(6x). +C x In(6x) (b) Evaluate the integral / edx using the substitution u = -9x. e- 27 dx = +CEvaluate the integral using an appropriate substitution. NOTE: Enter the exact anawcr. Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. [WNW+0