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Use the comparison method to show that the integral diverges.

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The integral from 1 to 8 of: (1+sin^2(x))/sqrt(x)

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hard to do ...since it converges......( 1 + sin² x ) / √ x ≤ 2 / √ x...and int over x in [ 1 , 8 ] of {
2 / √x dx } is 8√2 - 4....if you meant over [ 1 , ∞ ) then it does diverge since 1 / √x ≤ ( 1 + sin² x ) / √x

            
        

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