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Math Help - A Nasty integral -

  1. #1
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    Arrow A Nasty integral -

    Any Ideas on how to Approach this one? ...

    \int\sqrt{[1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}}du

    We have a sech(u) and its derivative -tanh(u)sech(u) and this suggests some sort of substitution maybe, but the radical makes it a bit nasty for Me.

    Any Ideas? ...Thanks Heaps,
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  2. #2
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    Quote Originally Posted by WalkingInMud View Post
    Any Ideas on how to Approach this one? ...

    \int\sqrt{[1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}}du

    We have a sech(u) and its derivative -tanh(u)sech(u) and this suggests some sort of substitution maybe, but the radical makes it a bit nasty for Me.

    Any Ideas? ...Thanks Heaps,
    Thinking out loud here, but simplify the radical...

    [1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}

    1-2sech(u)+sech^2(u)+tanh^2(u)sech^2(u)

    Use trig substitution: tanh^2(u)=sech^2(u)-1

    1-2sech(u)+sech^2(u)+[sech^2(u)-1]sech^2(u)

    1-2sech(u)+sech^2(u)+sech^4(u)-sech^2(u)

    1-2sech(u)+sech^4(u)

    Now, what can we do about that?
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  3. #3
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    Quote Originally Posted by colby2152 View Post
    [snip]Now, what can we do about that?
    A leading question ....?
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