A contribution to Coxeter

Calculus (Integrals, Series)
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Tolaso J Kos
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A contribution to Coxeter

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Post by Tolaso J Kos »

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.
Imagination is much more important than knowledge.
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