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    Little bit of trouble with this one. Nearly there though

    Intergrate with respect to x: (Q11 P5 ex 2A)

    coth^2 (x/2)

    This is what I have got:

    => INT cosech^2 (x/2) +1 dx
    = INT [sinh (x/2)]^-2 +1 dx
    = -(sinh (x/2))^-1 / (0.5cosh(x/2) + x + C <= this is where I think I have gone wrong

    = -2/[cosh (x/2)sinh (x/2)] + x + C

    This cosh (x/2) is supposed to be on the top of the fraction so it simplifies to coth. cant see how to get it up there though :'(


    Also, another one Q 26 in P5 ex 3A I get the final answer as 0.5 arctan(sinh 2x) + C whilst the answer has it as arctan e ^2x. Are these the same?
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    What board is it from? I'm doing edexcel and we are supposed to know that

    d(coth(x))/dx = -cosech²x (it's in FB but as trig instead of hyperbolic so can just look at that to help remember)

    So from the second line on your working

    ∫(cosech²(x/2) + 1)dx
    = -2coth(x/2) + x
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    Ahhhhhh, I saw that cot x => -cosec^2 x but not coth . Are all the trig ones the same as hyperbolic ones?

    Also, tried it a different way and reduced to:

    => 2 INT 1/(coshx - 1) dx Can anyone solve that one? Do you have to use the t substitution? t = tanh x/2? If so, are the sinh and cosh functions the equilivilent of the trig functions?

    e.g. sin A = 2t/1+t^2 ==> sinh A = 2t/1+t^2?
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    (Original post by Womble548)
    Ahhhhhh, I saw that cot x => -cosec^2 x but not coth . Are all the trig ones the same as hyperbolic ones?

    Also, tried it a different way and reduced to:

    => 2 INT 1/(coshx - 1) dx Can anyone solve that one? Do you have to use the t substitution? t = tanh x/2? If so, are the sinh and cosh functions the equilivilent of the trig functions?

    e.g. sin A = 2t/1+t^2 ==> sinh A = 2t/1+t^2?
    i'm confused about that so when do you apply osbournes rule?

    only in identities? and not in calculus?
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    (Original post by Phil23)
    i'm confused about that so when do you apply osbournes rule?

    only in identities? and not in calculus?
    Dunno?!
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    I don't think they are nescesarily going to the the same as trig in calculus and I think osbournes rule is only for identities.

    I just use the fact they are similar to help remember, and remember which ones arent the same.

    d(sech(x))/dx = -tanh(x)sech(x)

    and

    d(sec(x))/dx = tan(x)sec(x)

    So they arent all the same, and that one doesnt seem to follow osbournes rule?

    I dunno whether there is a rule for the calculus ones. Hopefully someone who knows what they're on about will help us
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    (Original post by Womble548)
    Dunno?!
    Osborne's rule is only valid for identities n NOT for calculus!

    there isnt any hard n fast rule for calculus, but more often than not they r comparable
 
 
 
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