Finding values of a for convergent integral from 1 to infinity

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erogol
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[tex]\int (((ax^2)/(x^3)+5) + 2 / x^3) dx[/tex] (one to infinite integral) find the all possible values of a?
 
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Is this supposed to be:


[tex]\int_{1}^{\infty}\left({\frac{ax^2}{x^3+5}+\frac{2}{x^3}\right)dx[/tex]

>??