A company's marginal cost function is MC(x) = and its fixed costs are 250. Find the cost function. 9x+1 Step 1 We want to find the cost function from the marginal cost. From the text, we know that the cost is the integral of the marginal cost. The integral we need is thus C(x) = 1 dx. MC(x) dx = 9x+1 9x+1 Step 2 Since the integrand is somewhat complicated, we try a u substitution. The denominator is a good guess, so we try that first. Setting u =9x+1, we find the differential, du = 9 dx. Solving for dx, we have dx = 1/9 1/9 du. Step 3 Substituting u and du into our integral, we have the following. C(x) = dx = C(u) = . 9x+1 du