Evaluate the following integral: \( \displaystyle \int_{0}^{\infty }\frac{\ln \left ( 1+\sigma x \right )\ln\left ( 1+\omega x^2 \right )}{x^3}\, dx \).
Perhaps you can come up with a clever approach. I tried Liebniz, got somewhere don't know how to continue, which is real shame!
\( \int_{0}^{\infty }\frac{\ln ( 1+\sigma x )\ln ( 1+\omega x^2 )}{x^3}\, dx \)
- Tolaso J Kos
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\( \int_{0}^{\infty }\frac{\ln ( 1+\sigma x )\ln ( 1+\omega x^2 )}{x^3}\, dx \)
Imagination is much more important than knowledge.
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