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Math Help - Having trouble with these!

  1. #1
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    Having trouble with these!

    1. Show that (coshx + sinhx)[to the power of] n = coshnx + sinhnx

    2. Determine the integral of tanhxdx

    3. Determine the integral of 4dx/(e to the x + e to the -x)squared



    PS How can i use the proper math symbols?!!

    Thanks!
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  2. #2
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    Quote Originally Posted by dannyshox View Post
    1. Show that (coshx + sinhx)[to the power of] n = coshnx + sinhnx

    This is trivial applying the definition of the hyperbolic functions

    2. Determine the integral of tanhxdx

    \tanh x=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^{2x}-1}{e^{2x}+1}=1-\frac{2}{e^{2x}+1}.
    Take it from here now (if you know integrals of usual trigonometric functions this one won't surprise you).


    3. Determine the integral of 4dx/(e to the x + e to the -x)squared

    [colo=blue]Get some ideas from the above

    Tonio[/color]



    PS How can i use the proper math symbols?!!


    Using LaTex


    Thanks!
    .
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  3. #3
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    I dont understand how u got that in 2.! I was looking at other examples and they use substitution?

    Also would it be right to use inegrations by parts in 3.?
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  4. #4
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    Quote Originally Posted by dannyshox View Post
    I dont understand how u got that in 2.! I was looking at other examples and they use substitution?

    Also would it be right to use inegrations by parts in 3.?
    For 2.- Multiply by \frac{e^x}{e^x}

    For 3.- You can try parts or note that =\frac{4}{e^x+e^{-x}}=\frac{1}{\cosh^2x}=\sec \!\!h^2x

    Tonio
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  5. #5
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    thanks
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