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Consider the following integral:

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

And consider the 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 .

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

See ; Related : https://math.stackexchange.com/q/3570663/702232

Note : Can't calculate the first integral on Mathematica for large values

Consider the following integral:

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

And consider the 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 three graphs in one axis system , so that I can compare)

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

See ; Related : https://math.stackexchange.com/q/3570663/702232

Note : Can't calculate the first integral on Mathematica for large values

Consider the following integral:

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

And consider the 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 .

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

See ; Related : https://math.stackexchange.com/q/3570663/702232

Consider the following integral:

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

And consider the 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 .

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

See ; Related : https://math.stackexchange.com/q/3570663/702232

Note : Can't calculate the first integral on Mathematica for large values