Evaluating the improper integral using must know basic techniques

[@slavinojunepri7648]

Excellent

[@graf_paper]

This is a classic!! The Gudermannian Function, which relates the area of the circular sector to the area of the hyperbolic sector!
gf(x) = \int_{0}^{x} 1/(cosh(t)) dt
I was just looking at this this morning.

[@cipherunity]

Thanks for sharing this information

[@holyshit922]

1/cosh(x)=cosh(x)/cosh^2(x)
cosh^2(x) - sinh^2(x) = 1
cosh^2(x) = 1 + sinh^2(x)
cosh(x) is even so we have
2\int_{0}^{\infty}\frac{cosh(x)}{1+sinh^2(x)}dx
2arctan(sinh(x))|_{0}^{\infty} = \pi

[@cipherunity]

That is perfect.

[@cipherunity]

It is done