令 √(1+x) = u,1+x = u²,dx = 2udu
∫x√(1+x)dx
=∫(u²-1)u×2udu
=2∫(u⁴- u²)du
=2[(u^5)/5 - u³/3] + C
=(2/5)[√(1+x)]^5- ⅔[√(1+x)]³ + C
经验证,答案准确无误.