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Math Help - [SOLVED] partial fraction with e^x

  1. #1
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    [SOLVED] partial fraction with e^x

    integrate (e^2x)/(e^2x + 3e^x + 2)
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by twilightstr View Post
    integrate (e^2x)/(e^2x + 3e^x + 2)
    Put e^x =t
    so e^xdx =dt
    hence
     <br />
dx=dt/t<br />

     <br />
\int{\frac{t^2dt}{(t^2+3t+2)t}}<br />

     <br />
=\int{\frac{tdt}{(t^2+3t+2)}}<br /> <br />

    =\int{\frac{tdt}{(t^2+2t+t+2)}}

     <br />
=\int{\frac{tdt}{(t(t+2)+(t+2))}}<br />

     <br />
=\int{\frac{tdt}{(t+1)(t+2)}}<br />

    go ahead infact the factorisation is not required at this stage
    Last edited by ADARSH; February 12th 2009 at 12:42 AM. Reason: added
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  3. #3
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    is the answer -lnle^x+1l + 2lnle^x+2l + c ?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by twilightstr View Post
    is the answer -lnle^x+1l + 2lnle^x+2l + c ?
    yes
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  5. #5
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    You can dispense the absolute value bars since those quantities are always positive.
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