res1 :=Integrate[Sinh[2*x]/(Exp[3*x] - 1),{x,0,Infinity}]
res1

N[res1]

NIntegrate[Sinh[2*x]/(Exp[3*x] - 1),{x,0,Infinity}]

res2 := Integrate[x*(Sqrt[x] -1/Sqrt[x])/( 1 - x^2),{x,0,1}]

res2

N[res2]

NIntegrate[(Sqrt[x] -1/Sqrt[x])/( 1 - x^2),{x,0,1}]