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

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Answer 1 · 2016-12-12T22:07:00

$intsecy(tany-secy)dy$

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

$=intsecytanydy-intsec^2ydy$

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

$=secy-tany+C$

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