1 answer

How do you integrate #int secy(tany-secy)dy#?

Question:

How do you integrate #int secy(tany-secy)dy#?

Answers

#intsecy(tany-secy)dy#

#=int(secytany-sec^2y)dy#

#=intsecytanydy-intsec^2ydy#

Since #d/dysecy=secytany#, we see that #intsecytany=secy#. Similarly, since #d/dytany=sec^2y#, we see that #intsec^2ydy=tany#.

#=secy-tany+C#

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