Answer
The integral diverges.
Work Step by Step
We know that x^{4}-x 1\div(x^{4}).
Multiplying both sides by x-1 and square rooting the denominator, we get x+1\div \sqrt[y] ((x^{4}-x))> x+1\div \sqry[y] ((x^{4})). So we get an inequality of the form f(x)>g(x)
Simplifying (x+1)\divsqrt[y]((x^{4})), we get 1\divx^{2}+1\divx. We know that 1\divx^{2} converges while 1\divx^{1} diverges. Since g(x)< f(x) and g(x) diverges, so we can say that f(x) also diverges. Hence, overall, the integral diverges in compliance with the comparison Theorem Test.
