求解∫(t^3)*{[1+4(t^2)]^(1/2)}dt
问题描述：
求解∫(t^3)*{[1+4(t^2)]^(1/2)}dt
答
∫ t³ * √(1+4t²) dt
= ∫ t² * √(1+4t²) d(t²/2)
= (1/2)(1/4)∫ 4t² * √(1+4t²) d(t²)
= (1/8)∫ (1+4t²-1) * √(1+4t²) d(t²)
= (1/32)∫ [(1+4t²)^(3/2) - √(1+4t²)] d(1+4t²)
= (1/32)(2/5)(1+4t²)^(5/2) - (1/32)(2/3)(1+4t²)^(3/2) + C
= (1/120)(6t²-1)(1+4t²)^(3/2) + C