Do I need to use McLaurin to solve the integral $ int frace^3 xx^3 dx$. [duplicate]

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  • Problem when integrating $e^x / x$.

    3 answers



I need to compute this primitive :




$$ int frace^3 xx^3 dx$$




but I don't know how to proceed. I tried an integration by part and get




$$ int frace^3xx dx$$




but then I am stuck... Is there no way else than making a McLaurin development ?



Thanks




integration taylor-expansion




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marked as duplicate by Nosrati, Lord Shark the Unknown, José Carlos Santos, Theoretical Economist, Taroccoesbrocco Aug 19 at 20:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • It is not expressible with elementary functions.
    – Bernard
    Aug 19 at 9:00














up vote
5
down vote

favorite
1













This question already has an answer here:



  • Problem when integrating $e^x / x$.

    3 answers



I need to compute this primitive :




$$ int frace^3 xx^3 dx$$




but I don't know how to proceed. I tried an integration by part and get




$$ int frace^3xx dx$$




but then I am stuck... Is there no way else than making a McLaurin development ?



Thanks




integration taylor-expansion




share|cite|improve this question














marked as duplicate by Nosrati, Lord Shark the Unknown, José Carlos Santos, Theoretical Economist, Taroccoesbrocco Aug 19 at 20:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • It is not expressible with elementary functions.
    – Bernard
    Aug 19 at 9:00












up vote
5
down vote

favorite
1









up vote
5
down vote

favorite
1






1






This question already has an answer here:



  • Problem when integrating $e^x / x$.

    3 answers



I need to compute this primitive :




$$ int frace^3 xx^3 dx$$




but I don't know how to proceed. I tried an integration by part and get




$$ int frace^3xx dx$$




but then I am stuck... Is there no way else than making a McLaurin development ?



Thanks




integration taylor-expansion




share|cite|improve this question















This question already has an answer here:



  • Problem when integrating $e^x / x$.

    3 answers



I need to compute this primitive :




$$ int frace^3 xx^3 dx$$




but I don't know how to proceed. I tried an integration by part and get




$$ int frace^3xx dx$$




but then I am stuck... Is there no way else than making a McLaurin development ?



Thanks





This question already has an answer here:



  • Problem when integrating $e^x / x$.

    3 answers





integration taylor-expansion





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 19 at 9:57









Nosrati

20.7k41644




20.7k41644










asked Aug 19 at 8:57









MysteryGuy

377215




377215




marked as duplicate by Nosrati, Lord Shark the Unknown, José Carlos Santos, Theoretical Economist, Taroccoesbrocco Aug 19 at 20:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.






marked as duplicate by Nosrati, Lord Shark the Unknown, José Carlos Santos, Theoretical Economist, Taroccoesbrocco Aug 19 at 20:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.













  • It is not expressible with elementary functions.
    – Bernard
    Aug 19 at 9:00
















  • It is not expressible with elementary functions.
    – Bernard
    Aug 19 at 9:00















It is not expressible with elementary functions.
– Bernard
Aug 19 at 9:00




It is not expressible with elementary functions.
– Bernard
Aug 19 at 9:00










2 Answers
2






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up vote
1
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$$int frace^xx dx$$ is not expressible in terms of elementary functions. Mathematicians define $$ Ei(x) = -int_-x^infty frace^-tt dt $$



Then one has that



$$int_- infty ^x frace^xx^3 dx $$
$$ = - frac12( x^-2 + 3 x^-1 ) e^3x -27Ei(3x) $$



(using Integration By Parts).






share|cite|improve this answer



























    up vote
    0
    down vote













    Always give a try to "the integrator"



    https://www.wolframalpha.com/input/?i=integrate+exp(3*x)%2F(x%5E3)



    A special function is needed for the analytic expression, see https://en.wikipedia.org/wiki/Exponential_integral






    share|cite|improve this answer





























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      1
      down vote













      $$int frace^xx dx$$ is not expressible in terms of elementary functions. Mathematicians define $$ Ei(x) = -int_-x^infty frace^-tt dt $$



      Then one has that



      $$int_- infty ^x frace^xx^3 dx $$
      $$ = - frac12( x^-2 + 3 x^-1 ) e^3x -27Ei(3x) $$



      (using Integration By Parts).






      share|cite|improve this answer
























        up vote
        1
        down vote













        $$int frace^xx dx$$ is not expressible in terms of elementary functions. Mathematicians define $$ Ei(x) = -int_-x^infty frace^-tt dt $$



        Then one has that



        $$int_- infty ^x frace^xx^3 dx $$
        $$ = - frac12( x^-2 + 3 x^-1 ) e^3x -27Ei(3x) $$



        (using Integration By Parts).






        share|cite|improve this answer






















          up vote
          1
          down vote










          up vote
          1
          down vote









          $$int frace^xx dx$$ is not expressible in terms of elementary functions. Mathematicians define $$ Ei(x) = -int_-x^infty frace^-tt dt $$



          Then one has that



          $$int_- infty ^x frace^xx^3 dx $$
          $$ = - frac12( x^-2 + 3 x^-1 ) e^3x -27Ei(3x) $$



          (using Integration By Parts).






          share|cite|improve this answer












          $$int frace^xx dx$$ is not expressible in terms of elementary functions. Mathematicians define $$ Ei(x) = -int_-x^infty frace^-tt dt $$



          Then one has that



          $$int_- infty ^x frace^xx^3 dx $$
          $$ = - frac12( x^-2 + 3 x^-1 ) e^3x -27Ei(3x) $$



          (using Integration By Parts).







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 19 at 10:38









          Arun Soor

          312




          312




















              up vote
              0
              down vote













              Always give a try to "the integrator"



              https://www.wolframalpha.com/input/?i=integrate+exp(3*x)%2F(x%5E3)



              A special function is needed for the analytic expression, see https://en.wikipedia.org/wiki/Exponential_integral






              share|cite|improve this answer


























                up vote
                0
                down vote













                Always give a try to "the integrator"



                https://www.wolframalpha.com/input/?i=integrate+exp(3*x)%2F(x%5E3)



                A special function is needed for the analytic expression, see https://en.wikipedia.org/wiki/Exponential_integral






                share|cite|improve this answer
























                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Always give a try to "the integrator"



                  https://www.wolframalpha.com/input/?i=integrate+exp(3*x)%2F(x%5E3)



                  A special function is needed for the analytic expression, see https://en.wikipedia.org/wiki/Exponential_integral






                  share|cite|improve this answer














                  Always give a try to "the integrator"



                  https://www.wolframalpha.com/input/?i=integrate+exp(3*x)%2F(x%5E3)



                  A special function is needed for the analytic expression, see https://en.wikipedia.org/wiki/Exponential_integral







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Aug 19 at 10:13









                  paulplusx

                  13312




                  13312










                  answered Aug 19 at 9:06









                  Laurent

                  127




                  127












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