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# worksheet2ans - 51 tan3 d (1) 1 3 (2) 51 2 5earctan y dy 1...

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(1) Z 51 tan 3 θdθ 51 2 tan 2 θ + ln | cos θ | + C (2) Z 1 3 - 1 5 e arctan y 1 + y 2 dy 5 e π 6 - 5 e - π 4 + C (3) Z 9 xdx x 4 + x 2 + 4 3 15 5 arctan( 2 x 2 +1 15 ) + C (4) Z 1 0 (1 + x ) 8 dx 4097 45 (5) Z 6 ln( x 2 - 25) 6 x ln( x 2 - 25) - 12 x + 30 ln( x +5 x - 5 ) + C (6) Z 18 dx e x + 18 x - ln(18 + e x ) + C (7) Z θ tan 2 θdθ θ tan θ - θ 2 2 + ln | cos θ | + C (8) Z 5 9 + e x dx 10 9 + e x + 15 x - 30 ln( e x + 9 + 3) + C or 10 9 + e x - 15 x + 30 ln( e x + 9 - 3) + C or 10 9 + e x + 15 ln | 9+ e x - 3 9+ e x +3 | + C (9) Z 4 x 5 e - x 3 dx - 4 3 e - x 3 ( x 3 + 1) + C (10) Z dx x 6 x + 49 1 7 ln | 6 x +49 - 7 6 x +49+7 | + C Evaluate the Improper integrals (1) Z 1 4 dx (5 x + 1) 2 2 15 1

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(2) Z 0 xdx ( x 2 + 32) 2 1 64 (3) Z 4 25 e - y/ 2 dy 50 e - 2 (4) Z 0 5 dz z 2 + 7 z + 6 ln(6) (5) Z 1 37 ln x x dx Diverges Evaluate the following limits, State if they exist or not, if not state why
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## This note was uploaded on 02/14/2012 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.

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worksheet2ans - 51 tan3 d (1) 1 3 (2) 51 2 5earctan y dy 1...

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