Putnam 1978 A3

Find the value of $k\ (0<k<5)$ such that $\int_0^{\infty} \frac{x^k}{2+4x+3x^2+5x^3+3x^4+4x^5+2x^6}\ dx$ is minimal.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.