In[6]:=
Clear[f,x]f[x_Real]=Simplify[x*(x^2+9/4)/((x^2+3/2+x*Sqrt[x^2+2])*Sqrt[x^2+2]),x>=0]Evaluate[f[5]]Plot[f[x],{x,0,5},{PlotRange->Full,ImageSize->Medium}]Simplify[NIntegrate[f[x],{x,0,5}]]
Out[7]=
x+
2
x
9
4
2
x
2
x
2
x
3
2
Out[8]=
f(5)
Out[9]=
Out[10]=
2.26493