A contribution to Coxeter
Posted: Sat Jul 09, 2016 5:28 am
As the title says the integral that follows is a Coxeter's one:
Prove that: \( \displaystyle \int_{1}^{6}\frac{\sec^{-1} t}{\left ( t+2 \right )\sqrt{t+1}}\left [ \frac{1}{\sqrt{t+3}}+2 \right ]\, dt=\frac{2\pi^2}{15} \)
The solution that I have is a little incomplete... I don't understand a step of the proof.
There is also exist a generalization of the above integral, which is used in the computation of that.
Prove that: \( \displaystyle \int_{1}^{6}\frac{\sec^{-1} t}{\left ( t+2 \right )\sqrt{t+1}}\left [ \frac{1}{\sqrt{t+3}}+2 \right ]\, dt=\frac{2\pi^2}{15} \)
The solution that I have is a little incomplete... I don't understand a step of the proof.
There is also exist a generalization of the above integral, which is used in the computation of that.