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Math Help - Hyperbolic integral

  1. #1
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    Hyperbolic integral

    Ok so:
    Its a 3 part question. I've completed parts 1 and 2.
    Part 1)
    Draw tanhx and tanh^-1 x on the same graph
    Part 2)
    Find  INT tanh x dx between limits k and 0 (where k > 0) which gives you ln coshk

    Part 3) though...
    I need to show  I tanh^-1 x dx between tanhk and 0 is ktanhk - ln coshk

    If you integrate it by parts you form:  [xtanh^-1 x] tanhk -> 0 = ktanhk and I t
    hink - int x/(1-x^2) between the same limits. I can't work out how to link lncoshk and that integral. And with the previous parts in the question.

    Thanks in advance!

    P.S How do you do an integral sign on this forum
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  2. #2
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    Re: Hyperbolic integral

    What have you tried? Show us some workings.

    Quote Originally Posted by Mrhappysmile View Post
    P.S How do you do an integral sign on this forum
    use \int command in LaTeX
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  3. #3
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    Re: Hyperbolic integral

    Quote Originally Posted by Mrhappysmile View Post
    I can't work out how to link lncoshk and that integral. And with the previous parts in the question.
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  4. #4
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    Re: Hyperbolic integral

    Ah I see so Instead of working it out as an integral. You have a rectangle of total area ktanhk and you're subtracting what you know from the previous parts. (The shaded area which is lncoshk). Hence ktanhk - lncoshk.

    Thanks!
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  5. #5
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    Re: Hyperbolic integral

    Quote Originally Posted by pickslides View Post

    use \int command in LaTeX
    Thanks
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