∫ dx/(1 + 9x²)
= (1/3)∫ d(3x)/[1 + (3x)²]
= (1/3)arctan(3x) + C,公式∫ 1/(a² + x²) dx = (1/a)arctan(x/a) + C
或详细：
令3x = tanθ,3dx = sec²θdθ
∫ dx/(1 + 9x²)
= ∫ (sec²θ)/3 * 1/(1 + tan²θ) dθ
= (1/3)∫ sec²θ/sec²θ dθ
= θ/3 + C
= (1/3)arctan(3x) + C
∫ dx/(1 + 9x²)
= (1/3)∫ d(3x)/[1 + (3x)²]
= (1/3)arctan(3x) + C,公式∫ 1/(a² + x²) dx = (1/a)arctan(x/a) + C
或详细：
令3x = tanθ,3dx = sec²θdθ
∫ dx/(1 + 9x²)
= ∫ (sec²θ)/3 * 1/(1 + tan²θ) dθ
= (1/3)∫ sec²θ/sec²θ dθ
= θ/3 + C
= (1/3)arctan(3x) + C