The question goes:

Suppose the continuous random variable X has a probability density function (PDF)

$\displaystyle f_{X}(x)=\frac{c}{x^6}, x>1$

i) Show that for X to be a valid PDF, $\displaystyle c$ must be equal to $\displaystyle 5$.

ii) Calculate $\displaystyle E(X^6e^{-2X})$.

For part i) I keep getting $\displaystyle -5$, not $\displaystyle 5$ for $\displaystyle c$, and I just can't fathom out part ii)