# value of k in definite Integration

#### jacks

##### Well-known member
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.