∫(0,1) x√(1+4x^2) dx
=(1/2)*∫(0,1) √(1+4x^2) d(x^2)
=(1/8)*∫(0,1) √(1+4x^2) d(4x^2)
=(1/8)*∫(0,1) (1+4x^2)^(1/2) d(4x^2+1)
=(1/8)*(2/3)*(1+4x^2)^(3/2) | (0,1)
=(1/12)*(5^(3/2)-1)
有不懂欢迎追问
∫(0,1) x√(1+4x^2) dx
=(1/2)*∫(0,1) √(1+4x^2) d(x^2)
=(1/8)*∫(0,1) √(1+4x^2) d(4x^2)
=(1/8)*∫(0,1) (1+4x^2)^(1/2) d(4x^2+1)
=(1/8)*(2/3)*(1+4x^2)^(3/2) | (0,1)
=(1/12)*(5^(3/2)-1)
有不懂欢迎追问