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Thread: Integral of sec^3(x) without reduction

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    Integral of sec^3(x) without reduction

    Can anyone help me integrate sec^3(x) without using the reduction formula?
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    Re: Integral of sec^3(x) without reduction

    do you allow integration by parts?
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    Re: Integral of sec^3(x) without reduction

    Yea no problem, only issue I have is with just going straight to a reduction formula, I want to see how the answer progresses to the solution rather than going from a -> b.
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    Re: Integral of sec^3(x) without reduction

    I think you can do it this way with IBP:

    Last edited by Drongoski; 9 Apr 2018 at 11:27 PM.
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    Integral of sec^3(x) without reduction

    Alternatively you can differentiate sec³x and then rearrange both sides and re-integrate. However this is essentially the same as Integration By parts.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: Integral of sec^3(x) without reduction

    "Inspection"
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    Re: Integral of sec^3(x) without reduction

    Quote Originally Posted by Drongoski View Post
    I think you can do it this way with IBP:

    Thanks for the reply, the way I progressed was going:



    And its at this point I get lost, I can get the sec integral fine, its given, but the integral is confusing
    Last edited by jjjcjjj892; 10 Apr 2018 at 12:41 AM.
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    Re: Integral of sec^3(x) without reduction

    Quote Originally Posted by jjjcjjj892 View Post
    Thanks for the reply, the way I progressed was going:



    And its at this point I get lost, I can get the sec integral fine, its given, but the integral is confusing
    use the identity tan^2(x) = sec^2(x) - 1
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    Re: Integral of sec^3(x) without reduction

    Spoiler (rollover to view):
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    Re: Integral of sec^3(x) without reduction

    that spoiler was a fail
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    Re: Integral of sec^3(x) without reduction

    Quote Originally Posted by Squar3root View Post
    Spoiler (rollover to view):
    Thank you, that made it very clear cheers everyone for the help.
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