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Q.
For $n \in N$, let $P_n=\int\limits_1^e(\ln x)^n d x$, then $\left(P_{10}-90 P_8\right)$ is equal to
Integrals
Solution:
$P _{ n }=\int\limits_1^{ c } \underset{\text { (I) }}{(\ln x )^{ n }} \underset{\text { (II) }}{1} \cdot dx $
$\Rightarrow P _{ n }= e - n P _{ n -1}$