If for n≥1, Pn=∫₁ˣ(logx)ⁿdx, then P₁₀ - P₈ is equal to :

Pₙ = ∫₁ˣ(logx)ⁿ
P₁₀ = ∫₁ˣ(logx)¹⁰ = ∫₁ˣt¹⁰eᵗdt = [t¹⁰eᵗ]₁ˣ - ∫₁ˣt⁹eᵗdt = e - [t⁹eᵗ]₁ˣ + 90∫₁ˣt⁸eᵗdt
→P₁₀ = e - e + 90P₁₀
→P₁₀ - P₁₀ = 10e