Where did I go wrong in my integration (by parts)?

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Working:



$int_^frac14x^2e^fracx4dx$



$u = x^2, fracdudx = 2x, fracdvdx = e^fracx4, v = 4e^fracx4$



$frac14left(4e^fracx4x^2-int :4e^fracx42xright)$



$int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



$int :4e^fracx4:2x:=:32xe^fracx4-32e^fracx4$



$therefore frac14int :x^2e^fracx4dx:=:frac14left(4e^fracx4x^2-32xe^fracx4+32e^fracx4right)+c$




integration proof-verification




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    Working:



    $int_^frac14x^2e^fracx4dx$



    $u = x^2, fracdudx = 2x, fracdvdx = e^fracx4, v = 4e^fracx4$



    $frac14left(4e^fracx4x^2-int :4e^fracx42xright)$



    $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



    $int :4e^fracx4:2x:=:32xe^fracx4-32e^fracx4$



    $therefore frac14int :x^2e^fracx4dx:=:frac14left(4e^fracx4x^2-32xe^fracx4+32e^fracx4right)+c$




    integration proof-verification




    share|cite|improve this question





















      up vote
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      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Working:



      $int_^frac14x^2e^fracx4dx$



      $u = x^2, fracdudx = 2x, fracdvdx = e^fracx4, v = 4e^fracx4$



      $frac14left(4e^fracx4x^2-int :4e^fracx42xright)$



      $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



      $int :4e^fracx4:2x:=:32xe^fracx4-32e^fracx4$



      $therefore frac14int :x^2e^fracx4dx:=:frac14left(4e^fracx4x^2-32xe^fracx4+32e^fracx4right)+c$




      integration proof-verification




      share|cite|improve this question











      Working:



      $int_^frac14x^2e^fracx4dx$



      $u = x^2, fracdudx = 2x, fracdvdx = e^fracx4, v = 4e^fracx4$



      $frac14left(4e^fracx4x^2-int :4e^fracx42xright)$



      $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



      $int :4e^fracx4:2x:=:32xe^fracx4-32e^fracx4$



      $therefore frac14int :x^2e^fracx4dx:=:frac14left(4e^fracx4x^2-32xe^fracx4+32e^fracx4right)+c$





      integration proof-verification





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      share|cite|improve this question




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      asked Jul 27 at 23:20









      Cheks Nweze

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          Starting from here:
          $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



          Note this next step that is different:



          $int :4e^fracx4:2x:=:32xe^fracx4-32int e^fracx4= :32xe^fracx4-128e^fracx4+C$



          You forgot to multiply by 4 when integrating $e^x/4$






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            1 Answer
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            1 Answer
            1






            active

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            active

            oldest

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            up vote
            2
            down vote



            accepted










            Starting from here:
            $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



            Note this next step that is different:



            $int :4e^fracx4:2x:=:32xe^fracx4-32int e^fracx4= :32xe^fracx4-128e^fracx4+C$



            You forgot to multiply by 4 when integrating $e^x/4$






            share|cite|improve this answer

























              up vote
              2
              down vote



              accepted










              Starting from here:
              $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



              Note this next step that is different:



              $int :4e^fracx4:2x:=:32xe^fracx4-32int e^fracx4= :32xe^fracx4-128e^fracx4+C$



              You forgot to multiply by 4 when integrating $e^x/4$






              share|cite|improve this answer























                up vote
                2
                down vote



                accepted







                up vote
                2
                down vote



                accepted






                Starting from here:
                $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



                Note this next step that is different:



                $int :4e^fracx4:2x:=:32xe^fracx4-32int e^fracx4= :32xe^fracx4-128e^fracx4+C$



                You forgot to multiply by 4 when integrating $e^x/4$






                share|cite|improve this answer













                Starting from here:
                $int :4e^fracx4:2x::u=2x,:fracdudx=2,:fracdvdx=4e^fracx4,:v=16e^fracx4$



                Note this next step that is different:



                $int :4e^fracx4:2x:=:32xe^fracx4-32int e^fracx4= :32xe^fracx4-128e^fracx4+C$



                You forgot to multiply by 4 when integrating $e^x/4$







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Jul 27 at 23:27









                MJW

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