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Thread: integration problem

  1. #1
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    integration problem

    Please Help me..

    Question 1:

    $\displaystyle
    \int {e^{-x}\ sinh(x)\ dx}

    $

    Question 2:
    $\displaystyle
    \int \frac {1}{\sqrt{1+x^2}}\ dx
    $

    Assume:
    $\displaystyle
    x = sinh (u)
    $
    $\displaystyle
    dx = cosh(u) du
    $

    Question 3:

    $\displaystyle
    \int \frac{1}{1-x^2} dx
    $

    Assume:
    $\displaystyle
    x=tanh(u)
    $
    $\displaystyle
    dx={sech^2} du
    $
    Last edited by cron1003; Apr 25th 2010 at 06:32 PM.
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  2. #2
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    Quote Originally Posted by cron1003 View Post
    Question 1:

    $\displaystyle
    \int e^{-x} \sinh(x) dx
    $
    change ... $\displaystyle \sinh(x) = \frac{e^x-e^{-x}}{2}$


    can't see your other images
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  3. #3
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    Quote Originally Posted by cron1003 View Post
    This is the other question

    Question 2:
    $\displaystyle
    \int \frac {1}{\sqrt{1+x^2}}\ dx
    $

    Assume:
    $\displaystyle
    x = sinh (u)
    $
    $\displaystyle
    dx = cosh(u) du
    $

    Question 3:
    $\displaystyle
    \int \frac{1}{1-x^2} dx
    $

    Assume:
    $\displaystyle
    x=tanh(u)
    $
    $\displaystyle
    dx={sech^2} du
    $
    Do what you are told to do (i.e. make the given substitutions) and then tell you stuck.
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  4. #4
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    Question 3:

    $\displaystyle
    \int \frac{1}{1-x^2} dx
    $

    $\displaystyle \frac{1}{1-x^2}=\frac{1}{2}(\frac{1}{1-x}-\frac{1}{1+x})$
    $\displaystyle
    \int \frac{1}{1-x^2} dx = \frac{1}{2}\int(\frac{1}{1-x}-\frac{1}{1+x})dx=\frac{1}{2}(ln|1-x|-ln|1+x|))=\frac{1}{2}ln|\frac{1-x}{1+x}|
    $
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  5. #5
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    Quote Originally Posted by cron1003 View Post
    Please Help me to solve this problem..

    Question 1:

    $\displaystyle
    \int {e^{-x}\ sinh(x)\ dx}
    $

    Question 2:

    $\displaystyle
    \int \frac {1}{\sqrt{1+x^2}}\ dx
    $

    Assume:
    $\displaystyle
    x = sinh (u)
    $
    $\displaystyle
    dx = cosh(u) du
    $

    Question 3:

    $\displaystyle
    \int \frac{1}{1-x^2} dx
    $

    Assume:
    $\displaystyle
    x=tanh(u)
    $
    $\displaystyle
    dx={sech^2} du
    $
    duplicate post ...

    http://www.mathhelpforum.com/math-he...n-problem.html
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  6. #6
    Master Of Puppets
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    Quote Originally Posted by cron1003 View Post
    Please Help me to solve this problem..

    Question 1:

    $\displaystyle
    \int e^{-x}\sinh x ~dx
    $
    Use the fact $\displaystyle \sinh x = \frac{e^x-e^{-x}}{2}$
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