At some point you've lost bracket in yours integral.On the assumption your function is as below, then:
f[x_] := Rationalize[1/(7.82 x + 11.6 x^(91/80) + 34.14 x^(91/60))]
NIntegrate[f[x], {x, 111, Infinity}, WorkingPrecision -> 50]
Out[1]= 0.0047720874548260654854177397600585533652154541290915.