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If `I_n = int(1/(a+x^2)^n)dx` show that; `I_(n+1) = x/(2an(a+x^2)^n)+(2n-1)/(2an)I_n`...

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If `I_n = int(1/(a+x^2)^n)dx` show that;

`I_(n+1) = x/(2an(a+x^2)^n)+(2n-1)/(2an)I_n`


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`` Integrating by parts ,considering  first function as `1/(a+x^2)^n` and 1 as second function


`=x/(a+x^2)^n+2n int x^2/(a+x^2)^{n+1}dx`

`` `=x/(a+x^2)^n+2n int(a+x^2-a)/(a+x^2)^{n+1}dx`









Thus we have proved the result.

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