AP Calculus BC 2019 Free Response question 5

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The title captures it all. In this video, I narrate my thoughts through the AP Calculus BC 2019 Free Response question 5. The concepts involved in this question are derivatives, rates of change, integration by partial fractions, and improper integrals with discontinuous integrands.

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Why wouldn’t you do complete the square on the denominator and using the arc tan formula?

akhilkumar