Below are attempts at u-substitution by students. Explain where each student went wrong, then explain how to solve the problem. (a) Jane is evaluating √ a(2x + 5)² dr. She identifies u = 2x + 5, so du = and so dx = du. Thus, ·S J x(2x+ 5)² dx = ²/2/² [x - u² du. Since the integral is 12 / 2 1 2dx, with respect to u, she treats x as a constant, and 1 3 x · u² du = 1⁄x · ²u²³ = ²√x(2x + 5)³. 2 3

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