How to find a positive maximum value of x in this function?

Questions
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1

So I have this function and I want to find the maximum value and the plot for T

sup.PNG

But I have difficulties with how I’m supposed to write an integral part of this function in Mathematica. I attempt to write the function, but it didn’t work. Here is the code I write :

Open in Wolfram Cloud ↗

r.nb (15.9 KB)

2

Your definition of f[x_] has x both as independent variable and as integration variable. You should use a different variable for the integral.