Consider the integral 5 x (z° +1) dx. In the following, we will evaluate the integral using two methods. Remember to write the arbitrary constant as "C". A. First, rewrite the integral by multiplying out the integrand: 52 ( +1) da = da !! Then evaluate the resulting integral term-by-term: 5x (a + 1) dr = B. Next, rewrite the integral using the substitution w = x + 1: 5a (2" + 1) da= dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: 5" ( +1) dz = C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.) (answer from B)-(answer from A) = Are bath of the answers correct? (Be sure you can explain why they are!)

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