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

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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
 
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!
 
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]
 
@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
 
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:

We won't do all the "discussing" for you!
 
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