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Math Help - integration problem

  1. #1
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    integration problem

    Please Help me..

    Question 1:

    <br />
\int {e^{-x}\ sinh(x)\ dx}<br /> <br />

    Question 2:
    <br />
\int \frac {1}{\sqrt{1+x^2}}\ dx<br />

    Assume:
    <br />
x = sinh (u)<br />
    <br />
dx = cosh(u) du<br />

    Question 3:

    <br />
\int \frac{1}{1-x^2} dx<br />

    Assume:
    <br />
x=tanh(u)<br />
    <br />
dx={sech^2} du<br />
    Last edited by cron1003; April 25th 2010 at 07:32 PM.
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  2. #2
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    Quote Originally Posted by cron1003 View Post
    Question 1:

    <br />
\int e^{-x} \sinh(x) dx<br />
    change ... \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:
    <br />
\int \frac {1}{\sqrt{1+x^2}}\ dx<br />

    Assume:
    <br />
x = sinh (u)<br />
    <br />
dx = cosh(u) du<br />

    Question 3:
    <br />
\int \frac{1}{1-x^2} dx<br />

    Assume:
    <br />
x=tanh(u)<br />
    <br />
dx={sech^2} du<br />
    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:

    <br />
\int \frac{1}{1-x^2} dx<br />

    \frac{1}{1-x^2}=\frac{1}{2}(\frac{1}{1-x}-\frac{1}{1+x})
    <br />
\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}|<br />
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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:

    <br />
\int {e^{-x}\ sinh(x)\ dx}<br />

    Question 2:

    <br />
\int \frac {1}{\sqrt{1+x^2}}\ dx<br />

    Assume:
    <br />
x = sinh (u)<br />
    <br />
dx = cosh(u) du<br />

    Question 3:

    <br />
\int \frac{1}{1-x^2} dx<br />

    Assume:
    <br />
x=tanh(u)<br />
    <br />
dx={sech^2} du<br />
    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:

    <br />
\int e^{-x}\sinh x ~dx<br />
    Use the fact \sinh x = \frac{e^x-e^{-x}}{2}
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