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Consider the integral methods. 1/42 4x4 (x + 1) dx. In the following, we will evaluate the integral using two A. First, rewrite the

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Consider the integral methods. 1/42 4x4 (x + 1) dx. In the following, we will evaluate the integral using two A. First, rewrite the integral by multiplying out the integrand: 4x4 (x + 1) dx = 9 [(4x+4x) dx Then evaluate the resulting integral term-by-term: [42*(2+) 10 5 4x (x + 1) dx 2x 4x = + +c 5 5 B. Next, rewrite the integral using the substitution w = x5 +1: [ 424 (26) 4x4 (x + 1) dx x = /Odw Evaluate this integral (and back-substitute for w) to find the value of the original integral: 4x (x + 1) dx == 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 both of the answers correct? (Be sure you can explain why they are!)

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