Explanation: 
Another Explanation (5):
সমাধান:
আমরা জানি, ∫dx/√(a²-x²) = sin⁻¹(x/a) + C
এখানে, ∫dx/√(16-9x²) = ∫dx/√(4²-(3x)²)
ধরি, 3x = 4sinθ
সুতরাং, 3dx = 4cosθ dθ
সুতরাং, dx = (4/3)cosθ dθ
এখন,
∫dx/√(16-9x²) = ∫(4/3)cosθ dθ / √(16-16sin²θ)
= ∫(4/3)cosθ dθ / √(16(1-sin²θ))
= ∫(4/3)cosθ dθ / (4√(cos²θ))
= ∫(4/3)cosθ dθ / (4cosθ)
= (1/3)∫dθ
= (1/3)θ + k
যেহেতু, 3x = 4sinθ
সুতরাং, sinθ = (3x)/4
সুতরাং, θ = sin⁻¹((3x)/4)
অতএব, ∫dx/√(16-9x²) = 1/3 sin⁻¹((3x)/4) + k 🎉
