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Math Help - Another trig integral

  1. #1
    Senior Member mollymcf2009's Avatar
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    Another trig integral

    Hey y'all,

    Ok, I'm stuck on another one:

    \int (tan(x))^3 sec(x) dx

    I usually try to take out one of the tan x and then do my u substitution with the sec x, but my du would be tanxsecx which would leave me with a sec x left over with my du. How should I tackle this one?

    Thanks!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Hey y'all,

    Ok, I'm stuck on another one:

    \int (tan(x))^3 sec(x) dx

    I usually try to take out one of the tan x and then do my u substitution with the sec x, but my du would be tanxsecx which would leave me with a sec x left over with my du. How should I tackle this one?

    Thanks!!
    Note that \tan^3 x \sec x = \tan x \tan^2 x \sec x = \tan x (\sec^2 x - 1) \sec x = (\sec^2 x - 1) \sec x \tan x

    now do you see it?
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