What is the integral of $logleft(x^{2} + k^{2}right)$ ?.












-2












$begingroup$


Where $displaystyle k$ is a real number ?. I have tried everything but I stuck when I have to find integral of
$k^{2}/left(x^{2} + k^{2}right)$.






real-analysis analysis







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    You may try $x^2 + k^2 = (x - jk) (x + jk)$ ...
    $endgroup$
    – Damien
    Dec 10 '18 at 16:17






  • 1




    $begingroup$
    try the substitution $x = ktan theta$
    $endgroup$
    – Doug M
    Dec 10 '18 at 18:10
















-2












$begingroup$


Where $displaystyle k$ is a real number ?. I have tried everything but I stuck when I have to find integral of
$k^{2}/left(x^{2} + k^{2}right)$.






real-analysis analysis







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    You may try $x^2 + k^2 = (x - jk) (x + jk)$ ...
    $endgroup$
    – Damien
    Dec 10 '18 at 16:17






  • 1




    $begingroup$
    try the substitution $x = ktan theta$
    $endgroup$
    – Doug M
    Dec 10 '18 at 18:10














-2












-2








-2





$begingroup$


Where $displaystyle k$ is a real number ?. I have tried everything but I stuck when I have to find integral of
$k^{2}/left(x^{2} + k^{2}right)$.






real-analysis analysis







share|cite|improve this question











$endgroup$




Where $displaystyle k$ is a real number ?. I have tried everything but I stuck when I have to find integral of
$k^{2}/left(x^{2} + k^{2}right)$.






real-analysis analysis




real-analysis analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 10 '18 at 19:26









Felix Marin

68.8k7109146




68.8k7109146










asked Dec 10 '18 at 15:49









Panagiotis PanagiotouPanagiotis Panagiotou

1




1








  • 2




    $begingroup$
    You may try $x^2 + k^2 = (x - jk) (x + jk)$ ...
    $endgroup$
    – Damien
    Dec 10 '18 at 16:17






  • 1




    $begingroup$
    try the substitution $x = ktan theta$
    $endgroup$
    – Doug M
    Dec 10 '18 at 18:10














  • 2




    $begingroup$
    You may try $x^2 + k^2 = (x - jk) (x + jk)$ ...
    $endgroup$
    – Damien
    Dec 10 '18 at 16:17






  • 1




    $begingroup$
    try the substitution $x = ktan theta$
    $endgroup$
    – Doug M
    Dec 10 '18 at 18:10








2




2




$begingroup$
You may try $x^2 + k^2 = (x - jk) (x + jk)$ ...
$endgroup$
– Damien
Dec 10 '18 at 16:17




$begingroup$
You may try $x^2 + k^2 = (x - jk) (x + jk)$ ...
$endgroup$
– Damien
Dec 10 '18 at 16:17




1




1




$begingroup$
try the substitution $x = ktan theta$
$endgroup$
– Doug M
Dec 10 '18 at 18:10




$begingroup$
try the substitution $x = ktan theta$
$endgroup$
– Doug M
Dec 10 '18 at 18:10










1 Answer
1






active

oldest

votes


















2












$begingroup$

Integrate by parts. $u=ln(x^2+k^2)$ and $dv=dx$ to change to the integral



$$int frac{2x^2}{x^2+k^2} ; dx$$



which is do-able by ordinary methods.






share|cite|improve this answer









$endgroup$













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    1 Answer
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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

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    active

    oldest

    votes









    2












    $begingroup$

    Integrate by parts. $u=ln(x^2+k^2)$ and $dv=dx$ to change to the integral



    $$int frac{2x^2}{x^2+k^2} ; dx$$



    which is do-able by ordinary methods.






    share|cite|improve this answer









    $endgroup$


















      2












      $begingroup$

      Integrate by parts. $u=ln(x^2+k^2)$ and $dv=dx$ to change to the integral



      $$int frac{2x^2}{x^2+k^2} ; dx$$



      which is do-able by ordinary methods.






      share|cite|improve this answer









      $endgroup$
















        2












        2








        2





        $begingroup$

        Integrate by parts. $u=ln(x^2+k^2)$ and $dv=dx$ to change to the integral



        $$int frac{2x^2}{x^2+k^2} ; dx$$



        which is do-able by ordinary methods.






        share|cite|improve this answer









        $endgroup$



        Integrate by parts. $u=ln(x^2+k^2)$ and $dv=dx$ to change to the integral



        $$int frac{2x^2}{x^2+k^2} ; dx$$



        which is do-able by ordinary methods.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 10 '18 at 19:35









        B. GoddardB. Goddard

        19.8k21442




        19.8k21442






























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