# Comparison of integrals with a function (at least numerically):

Consider the following integral:

$$S(q)=\int_{x=2}^q\sin^2\left(\frac{π\Gamma(x)}{2x}\right)dx$$

And consider functions :

$$R(q)=\frac{q}{\log(q)}$$

$$T(q)=\int_2^q\frac{1}{\log(x)}dx$$

I want to compare them with each other ( at least numerically for large interval of value )

If graph for very large intervals (upto atleast $$10^4$$) possible please add ( please add all the graph in one axis system so I can compare them ).

(Due to wild oscillations of $$S(q)$$; I can't deal with it )( Mathematica doesn't seem to help with large values ).

(Does numerics suggests $$S(q) \sim R(q)$$ or $$T(q)$$? ).

• If I understand correctly, you want a graph of those three function with $2\le q\le10^4$? – Jan Eerland May 7 at 13:55
• @Jan yes! That's what I want – Bambi May 7 at 13:57
• Why a close vote !? – Bambi May 7 at 13:58
• I already mentioned the link where all the details are mentioned , why to repeat again ? – Bambi May 7 at 14:06