Without integrating, determine whether the integral ∫1∞1x7+13\displaystyle {\int_{{1}}^{\infty}}\frac{{1}}{{\sqrt[{{3}}]{{{x}^{{7}}+{1}}}}}∫1∞3x7+11 converges or diverges by comparing the function f(x)=1x7+13\displaystyle {f{{\left({x}\right)}}}=\frac{{1}}{{\sqrt[{{3}}]{{{x}^{{7}}+{1}}}}}f(x)=3x7+11 with g(x)=1x73\displaystyle {g{{\left({x}\right)}}}=\frac{{1}}{{\sqrt[{{3}}]{{{x}^{{7}}}}}}g(x)=3x71 .
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