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leniorose
Blue Jay
Blue Jay

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Joined: 27 May 2014
Gender: Female
Posts: 96
Location: U.S.A

24 Sep 2017, 6:35 pm

Tricky question.
You could theoretically replace Sec(X) with an equivalent trig value, and then use integration by parts. You would still get a long answer, but sec(x) makes everything a bit tricky. Replacing it could prevent some confusion later.

As for why it's long, you would have to use integration by parts multiple times, because the equation gives you another integral as part of it's answer- so you have to do that integral by parts and combine like terms, over and over again until you get one that neatly integrates.