SOAL INTEGRAL NO SPAM

∫ dx / √(x² + 2x + 26) = ∫ dx / √[(x + 1)² + 25]
u² = x + 1, a² = 25

∫ du / √(a² + u²) = ..., a > 0
u / a = sinh θ → u = a sinh θ
du / dθ = a cosh θ → du = a cosh θ dθ
a + u² = a² [1 + (u / a)²] = a² (1 + sinh² θ) = a² cosh² θ
∫ du / √(a² + u²)
= ∫ a cosh θ dθ / (a cosh θ)
= ∫ dθ = θ + C = sinh⁻¹ (u / a)

∫ dx / √(x² + 2x + 26)
= ∫ dx / √[(x + 1)² + 25] = sinh⁻¹ [(x + 1) / 5]