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Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F (:17) and C(53) are antiderivatives of f (as) and gm) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, /cf(a:)ds: =cF(:c)+C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, _/lf(33) + 9($)] div = F(:r) + C(25) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [f (x) - g(x)] dx = F(x) - G(x) + C. prtl The power rule: [ x dx = +C,ry -1. r+1 NOTE: Enter the exact answer. 7 5x + dx = +C 8.74Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F (as) and C(55) are antiderivatives of x) and 9(12) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, fcx) d3: = cF(:r) + C. (b) An antiderivative of a sum is the sum of the antiderivatives, that is, /W) + m1 dm : M) + as) + c. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [f(x) - g(x)] dx = F(x) - G(x) + C. The power rule: x dx = + C,r -1. r+1 NOTE: Enter the exact answer. x 3 - 3x6 + 5x2 dx = +CEvaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F (32') and C(m) are antiderivatives of f (21:) and 9(33) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, /Cf(:r)d:c =cF(J:)+C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, [me + gm] aim = M) + are) + c. (c) An autiderivative of a difference is the difference of the antiderivatives; that is, [[1000 _ 9017)] d3? = F(:r:) C(33) + C_ \fEvaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. MW) +c Evaluate the integral and check your answer by differentiating. + 4x4- 1 dx = + CEvaluate the integral using an appmpriate substitution. NOTE: Enter the exact answer. fem1M = +0 Evaluate the integral using an apprOpriate substitution. N UTE: Enter the exact answer. Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 8 dx = +C (1 - 2.x) 4Evaluate the integral using an apprOpriate substitution. NOTE: Enter the exact answer. $3 / (53:4+4)5