Who can help me?

Questions
1

Numerical Integral, Integral[1/(7.82x+11.6x^(91/80) + 34.14x^(91/60), {x, 111, \infty} ]
Out[1] = -11.2317+0.777712 ?

What is the output ? namely, out[1] = -11.2317 ,or out[1] = 0.777712 ?

2

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.