المسالةبالمرفق

 

 

we know that the integral fro m 6 to infinity for the function 1 / x^ 3/2 is convergent
and the limit for ( 1 /(x^3 -5)^ 1/2 ) /(1 /x^ 3/2 ) when x tends to infinity =1 does not equal to 0
then the the given integral is convergent

 

 

the integral from 6 to infinity for the function 1 /x^(3/2) is convergent because the the power > 1

 

 

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we know that the integral fro m 6 to infinity for the function 1 / x^ 3/2 is convergent and the limit for ( 1 /(x^3 -5)^ 1/2 ) /(1 /x^ 3/2 ) when x tends to infinity =1 does not equal to 0 then the the given integral is convergent

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