Math 149 quiz 9 key v8 Problem 2 Let us define a function for the integrand of the indefinite integral expressed in terms of the new variable u In 10 f u D H1 12L 1 H2 u 10L In 11 f uD 1 Out 11 12 I2 u10 M Now let us ask Mathematica to evaluate this indefinite integral in terms of u Note that doing so was NOT part of the quiz problem 2 Quiz09S11key v8 nb In 12 Ju Integrate f uD uD 1 u Out 12 480 29 10 2 I1 2 I1 8 ArcTanA 21 10 5 M ArcTanB 5 M ArcTanB 2 I 1 5 M ArcTanB E 2 I 1 10 2 5 M ArcTanB 5 2 29 10 u 1 10 2 5 2 29 10 u 1 2 I5 F 5 F 5 5 M 2 29 10 u 1 F 5 u 24 5 u2 F 10 2 5 LogB2 22 5 5 5 10 2 5 LogB2 22 5 5 5 2 I5 5 M LogB2 22 5 5 5 u 24 5 u2 F 2 I5 5 M LogB2 22 5 5 5 u 24 5 u2 F u 24 5 u2 F Now let us ask Mathematica to check this result by differentiation 2 I5 5 M 2 29 10 u 1 5 F Quiz09S11key v8 nb In 13 DJu D Ju uD 4 29 10 1 Out 13 480 29 10 1 10 2 u2 21 5 10 2 5 5 2 24 5 u 2 22 5 22 5 5 22 5 5 5 5 5 u 24 5 2 I5 5 2 24 5 u u2 5M 22 5 5 5 2 24 5 u 2 22 5 2 I5 5M 5 u 24 5 u2 5 22 5 5 2 22 5 5 5 4 29 10 2 10 2 1 In 14 J1 5 N 1 24 12 u10 2 I1 u2 4 29 10 2 5 2 29 10 u Simplify DJuD Out 14 u 24 5 10 2 1 5 M 1 2 5M 2 J5 5 N 2 2 29 10 J1 5 N 2 4 29 10 2 J5 5 N 2 29 10 u 5 2 29 10 u J1 5 N u 24 5 u2 5 4 29 10 I 1 5 2 24 5 u 2 22 5 5 1 J 1 5 N 2 2 u 3
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