Convergence of $int_3^infty fracsin x log x,dx$ [closed]

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I can't think of any solution. I have tried comparison tests but none seems to work.



$$int_3^infty fracsin xlog x, dx$$
Can you think of any tests?




improper-integrals




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closed as unclear what you're asking by 5xum, Jack D'Aurizio♦ Aug 21 at 14:51


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 4




    What is the question?
    – 5xum
    Aug 21 at 12:53






  • 1




    I think Dirichlet's Test may be helpful here (assuming you are trying to show the integral converges).
    – Clayton
    Aug 21 at 13:13










  • @5xum the question is how to check its convergence or divergence
    – Sadil Khan
    Aug 21 at 13:41










  • The integral is convergent by Dirichlet's test. $sin(x)$ has a bounded primitive while $frac1log x$ is decreasing to zero on $[3,+infty)$.
    – Jack D'Aurizio♦
    Aug 21 at 14:51














up vote
-3
down vote

favorite












I can't think of any solution. I have tried comparison tests but none seems to work.



$$int_3^infty fracsin xlog x, dx$$
Can you think of any tests?




improper-integrals




share|cite|improve this question














closed as unclear what you're asking by 5xum, Jack D'Aurizio♦ Aug 21 at 14:51


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 4




    What is the question?
    – 5xum
    Aug 21 at 12:53






  • 1




    I think Dirichlet's Test may be helpful here (assuming you are trying to show the integral converges).
    – Clayton
    Aug 21 at 13:13










  • @5xum the question is how to check its convergence or divergence
    – Sadil Khan
    Aug 21 at 13:41










  • The integral is convergent by Dirichlet's test. $sin(x)$ has a bounded primitive while $frac1log x$ is decreasing to zero on $[3,+infty)$.
    – Jack D'Aurizio♦
    Aug 21 at 14:51












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











I can't think of any solution. I have tried comparison tests but none seems to work.



$$int_3^infty fracsin xlog x, dx$$
Can you think of any tests?




improper-integrals




share|cite|improve this question














I can't think of any solution. I have tried comparison tests but none seems to work.



$$int_3^infty fracsin xlog x, dx$$
Can you think of any tests?





improper-integrals





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 22 at 18:48

























asked Aug 21 at 12:50









Sadil Khan

3287




3287




closed as unclear what you're asking by 5xum, Jack D'Aurizio♦ Aug 21 at 14:51


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






closed as unclear what you're asking by 5xum, Jack D'Aurizio♦ Aug 21 at 14:51


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.









  • 4




    What is the question?
    – 5xum
    Aug 21 at 12:53






  • 1




    I think Dirichlet's Test may be helpful here (assuming you are trying to show the integral converges).
    – Clayton
    Aug 21 at 13:13










  • @5xum the question is how to check its convergence or divergence
    – Sadil Khan
    Aug 21 at 13:41










  • The integral is convergent by Dirichlet's test. $sin(x)$ has a bounded primitive while $frac1log x$ is decreasing to zero on $[3,+infty)$.
    – Jack D'Aurizio♦
    Aug 21 at 14:51












  • 4




    What is the question?
    – 5xum
    Aug 21 at 12:53






  • 1




    I think Dirichlet's Test may be helpful here (assuming you are trying to show the integral converges).
    – Clayton
    Aug 21 at 13:13










  • @5xum the question is how to check its convergence or divergence
    – Sadil Khan
    Aug 21 at 13:41










  • The integral is convergent by Dirichlet's test. $sin(x)$ has a bounded primitive while $frac1log x$ is decreasing to zero on $[3,+infty)$.
    – Jack D'Aurizio♦
    Aug 21 at 14:51







4




4




What is the question?
– 5xum
Aug 21 at 12:53




What is the question?
– 5xum
Aug 21 at 12:53




1




1




I think Dirichlet's Test may be helpful here (assuming you are trying to show the integral converges).
– Clayton
Aug 21 at 13:13




I think Dirichlet's Test may be helpful here (assuming you are trying to show the integral converges).
– Clayton
Aug 21 at 13:13












@5xum the question is how to check its convergence or divergence
– Sadil Khan
Aug 21 at 13:41




@5xum the question is how to check its convergence or divergence
– Sadil Khan
Aug 21 at 13:41












The integral is convergent by Dirichlet's test. $sin(x)$ has a bounded primitive while $frac1log x$ is decreasing to zero on $[3,+infty)$.
– Jack D'Aurizio♦
Aug 21 at 14:51




The integral is convergent by Dirichlet's test. $sin(x)$ has a bounded primitive while $frac1log x$ is decreasing to zero on $[3,+infty)$.
– Jack D'Aurizio♦
Aug 21 at 14:51










1 Answer
1






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up vote
1
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Hint:



Think about the sign of the integrating function on any single interval $[kpi, (k+1)pi]$.






share|cite|improve this answer



























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote













    Hint:



    Think about the sign of the integrating function on any single interval $[kpi, (k+1)pi]$.






    share|cite|improve this answer
























      up vote
      1
      down vote













      Hint:



      Think about the sign of the integrating function on any single interval $[kpi, (k+1)pi]$.






      share|cite|improve this answer






















        up vote
        1
        down vote










        up vote
        1
        down vote









        Hint:



        Think about the sign of the integrating function on any single interval $[kpi, (k+1)pi]$.






        share|cite|improve this answer












        Hint:



        Think about the sign of the integrating function on any single interval $[kpi, (k+1)pi]$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 21 at 13:46









        5xum

        82.5k383147




        82.5k383147












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