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(x) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, | ef(x) dx = cF(x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, |[f(x) + g(x)] dc = F(x)+ G(x)+ C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, |Lf(x) – g(x)] dr = F(x) – G(æ) +C. x"+1 +C,r + –1. r +1 The power rule: x" dx NOTE: Enter the exact answer. 7 dx = 8x4 7x + +C %3D

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