Pre-Calc Homework Solutions 470

Pre-Calc Homework Solutions 470 - 470 Appendix A6 1 ln (1 2...

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Unformatted text preview: 470 Appendix A6 1 ln (1 2 40. If y x tanh 1 x 1 x2) 1 x2 C, 1 2x 2 1 x2 49. Let u tanh 1 t t tanh t t 1/2 and du t 2 dt t . dy then dx tanh x x 1 x, sech dt C 2 sech u tanh u du 2 sech dt . t which verifies the formula. 41. Let u 2x and du 2 dx. cosh u 2 2( sech u) 50. Let u C cosh 2x 2 t C ln t and du sinh 2x dx 42. Let u sinh 43. Let u 1 sinh u du 2 1 dx. 5 C csch (ln t) coth (ln t) dt t csch u coth u du C x and du 5 x dx 5 csch u 5 cosh u 1 dx. 2 C csch (ln t) 5 sinh u du ln 3 and du ln 3 dx ln 3 C 5 cosh x 5 C 51. Let u sinh x, du e ln 2 2 e ln 4 2 ln 4 15/8 ln 2 3/4 cosh x dx, the lower limit is e ln 2 x 2 x 6 cosh 2 x 12 sinh 2 2 2 ln 4 sinh (ln 2) 12 sinh u C 1 2 12 cosh u du C 3 and the upper 4 4 2 1 4 limit is sinh (ln 4) ln 2 and du ln 2) dx ln 2) C 52. Let u cosh 0 7 ln cosh u C1 cosh (2 ln 2) 4 2 1 4 e 15 . 8 44. Let u 3x 3 dx. 4 cosh u du 3 4 sinh u 3 ln 4 4 cosh (3x 4 sinh (3x 3 C ln 2 coth x dx ln u 15/8 3/4 cosh x dx sinh x 15 3 ln ln 8 4 1 du u 15 4 ln 8 3 ln 5 2 0.916 45. Let u 1 x and du dx. 7 7 x sinh u tanh dx 7 du 7 cosh u x 7 ln cosh C1 7 x/7 x/7 e e 7 ln C1 2 cosh 2x, du 2 sinh (2x) dx, the lower limit is 1 and the upper limit is cosh (ln 4) 17 . 8 1 sinh 2x dx 0 2 cosh 2x 1 17 ln ln 1 2 8 ln 2 ln 2 17/8 1 e ln 4 2 e ln 4 7 ln e x/7 7 ln e x/7 e e x/7 x/7 7 ln 2 C d C1 ln 2 0 tanh 2x dx 1 17/8 ln u 2 1 1 du u 1 17 ln 2 8 0.377 46. Let u 3 and du d 3 . 3 ln sinh u e / 3 ln 2 coth 3 cosh u 3 du sinh u 3 53. C1 C1 ln 4 2e cosh ln 2 d 1) d ln 4 2e e 2 e ln 2 ln 4 d ln 4 (e 2 e 2 e 2 ln 4 2 3 ln sinh 3 ln e 3 ln e 47. Let u sech 2 C1 e e / 3 3 ln e 2 / 3 e 1 8 3 32 ln 2 2 ln 2 2 ln 2 ln 2 ln 2 1 32 2 ln 4 3 32 / 3 3 ln 2 C dx. 2 C1 ln 4 ln 2 2 ln 2 / 3 / 3 0.787 ln2 x x 1 and du 2 1 dx 2 1 C 2 54. tanh u C 0 4e ln 2 sinh (1 e 1 8 d e 2 1 2 2 0 4e 2 0 e 2 e 2 e 0 2 e ln 2 0 d sech u du 2 0 )d tanh x 48. Let u (5 2 2 ln 2 2 ln 2 dx. csch2 u du ( coth u) C 2 ln 2 x) and du x) dx C x) C csch2 (5 coth u coth (5 2 ln 2 1 4 1 ln 4 3 4 0.636 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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