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Problem Let f ( x ) = x ( 1 + x n ) 1 / n f(x) = \frac{x}{(1+x^n)^{1/n}} f ( x ) = ( 1 + x n ) 1/ n x n ≥ 2 n \ge 2 n ≥ 2 g ( x ) = f ∘ f ∘ f ∘ ⋯ ∘ f ⏟ n times ( x ) g(x) = \underbrace{f \circ f \circ f \circ \dots \circ f}_{n \text{ times}}(x) g ( x ) = n times f ∘ f ∘ f ∘ ⋯ ∘ f ( x ) ∫ x n − 2 g ( x ) d x \int x^{n-2} g(x) dx ∫ x n − 2 g ( x ) d x 1 n ( n − 1 ) ( 1 + n x n ) 1 − 1 n + C \frac{1}{n(n-1)} (1+nx^n)^{1-\frac{1}{n}} + C n ( n − 1 ) 1 ( 1 + n x n ) 1 − n 1 + C 1 n − 1 ( 1 + n x n ) 1 − 1 n + C \frac{1}{n-1} (1+nx^n)^{1-\frac{1}{n}} + C n − 1 1 ( 1 + n x n ) 1 − n 1 + C 1 n ( n + 1 ) ( 1 + n x n ) 1 + 1 n + C \frac{1}{n(n+1)} (1+nx^n)^{1+\frac{1}{n}} + C n ( n + 1 ) 1 ( 1 + n x n ) 1 + n 1 + C 1 n + 1 ( 1 + n x n ) 1 + 1 n + C \frac{1}{n+1} (1+nx^n)^{1+\frac{1}{n}} + C n + 1 1 ( 1 + n x n ) 1 + n 1 + C Browse the problem library