There are several ways to express the indefinite integral of sech x.

a. Show that ∫ sech x dx = tan^-1 (sinh x) + C (Theorem 6.9).

Writeand then make a change of variables.

b. Show that ∫ sech x dx = sin^-1 (tanh x) + C. Show that and then make a change of variables.

c. Verify that ∫ sech x dx = 2 tan^-1 e^x + C by proving d/dx (2 tan^-1 e^x) = sech x.

Transcribed Image Text:

cosh x cosh x sech x cosh? x 1 + sinh² x cosh x sech? x х Vi - tanh? x