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Math Help - How do I solve integral tanh(7x)?

  1. #1
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    How do I solve integral tanh(7x)?

    I have a long integral and broken it up and solved everything besides \int tanh 7x dx
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by circuscircus View Post
    I have a long integral and broken it up and solved everything besides \int tan 7x dx
    a simple substitution of t = 7x will do
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    a simple substitution of t = 7x will do
    Yea understood but the problem is my book gives the integrals for only sinh, cosh,sech^2,csc^2,sech, and csch but not tanh nor coth
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by circuscircus View Post
    Yea understood but the problem is my book gives the integrals for only sinh, cosh,sech^2,csc^2,sech, and csch but not tanh nor coth
    oh, you changed the question.

    note that \tanh x = \frac {\sinh x}{\cosh x}

    and it is still an easy substitution problem
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  5. #5
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    Dx tanh 7x

    = Dx \frac{sinh(7x)}{cosh(7x)}

    use quotient rule
    = \frac{7cosh(7x)cos(7x) - 7sinh(7x)sinh(7x)}{cosh(7x)^2}

    so is it like this?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by circuscircus View Post
    Dx tanh 7x

    = Dx \frac{sinh(7x)}{cosh(7x)}

    use quotient rule
    = \frac{7cosh(7x)cos(7x) - 7sinh(7x)sinh(7x)}{cosh(7x)^2}

    so is it like this?
    ......are you confused about something? or did you type the wrong question originally? you should be finding the integral, not taking the derivative
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  7. #7
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    OH man sorry I was out of it

    Yea, how would I solve the integral of e^x-e^-x / e^x+e^-x
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by circuscircus View Post
    OH man sorry I was out of it

    Yea, how would I solve the integral of e^x-e^-x / e^x+e^-x
    there is no need to write the formulas that way. just use the substitution u = \cosh x
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  9. #9
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    u = coshx
    du = sinhx

    1/u du

    ln |u| + C

    ln |coshx|+c

    Thanks!
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by circuscircus View Post
    u = coshx
    du = sinhx

    1/u du

    ln |u| + C

    ln |coshx|+c

    Thanks!
    not quite. remember, we are dealing with \tanh {\color {red}7}x

    but i think you have the idea
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