Improper integral: Discuss convergence of integral from 0 to + infinity of : log(x^4)/(|x^4-1|)^a by varying parameter 'a'

[Deleted member 108663]

Discuss the convergence of this integral by varying the parameter

a>=0
integral from 0 to + infinity of : log(x^4)/(|x^4-1|)^a

 

[stapel]

Discuss the convergence of this integral by varying the parameter

a>=0
integral from 0 to + infinity of : log(x^4)/(|x^4-1|)^a

Okay; let's discuss. What are your thoughts? What have you tried? How far have you gotten? Where are you getting stuck?

Please be complete. Thank you!

 

[pka]

Discuss the convergence of this integral by varying the parameter a>=0
integral from 0 to + infinity of : log(x^4)/(|x^4-1|)^a

@Marcello, please double check to be sure that the question is posted correctly .
[imath]\displaystyle\int_0^\infty {\frac{{\log \left( {{x^4}} \right)}}{{{{\left( {\left| {{x^4} - 1} \right|} \right)}^a}}}dx} ,\;a \geqslant 0[/imath]

 

[Deleted member 108663]

@Marcello, please double check to be sure that the question is posted correctly .

[imath]\displaystyle\int_0^\infty {\frac{{\log \left( {{x^4}} \right)}}{{{{\left( {\left| {{x^4} - 1} \right|} \right)}^a}}}dx} ,\;a \geqslant 0[/imath]

correct

 

[Dr.Peterson]

correct

So what have you learned about convergence of improper integrals? What method(s) have you tried? Where are you stuck?

It looks like you failed to read this:

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