∫ e u du n = Γ ( ) n . of - - Example . Evaluate n dx ∞ , where n is a positive integer ≥ . Using the formula n = e e n , we get I = x n dx ∞ ∞ ∞ ∞ Using the substitution u = x log , we get dx du = log When x = , we get u = .When x = ∞ , we get u = ∞ .
∴ I = e du ∞ (log ) e u du ∞ = Γ ( (log ) n n = n n ! (log ) + .