Many formulas There are several ways to express the
Chapter 6, Problem 107(choose chapter or problem)
Many formulas There are several ways to express the indefinite integral of sech x. a. Show that 1sech x dx = tan-11sinh x2 + C (Theorem 6.9). 1Hint: Write sech x = 1 cosh x = cosh x cosh2 x = cosh x 1 + sinh2 x and then make a change of variables.2 b. Show that 1sech x dx = sin-11tanh x2 + C. 1Hint: Show that sech x = sech2 x 21 - tanh2 x and then make a change of variables.2 c. Verify that 1sech x dx = 2 tan-1 ex + C by proving d dx 12 tan-1ex2 = sech x.
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