# Thread: value of k in definite Integration

1. Let $\displaystyle p(x)=2x^6+4x^5+3x^4+5x^3+3x^2+4x+2.$ Let $\displaystyle \displaystyle I_{k}=\int^{\infty}_{0}\frac{x^k}{p(x)}dx$

where $\displaystyle 0<k<5.$ Then value of $\displaystyle k$ for which $\displaystyle \displaystyle I_{k}$ is smallest.

2.