求分子是lnx,分母是(x的平方+1)的3/2次方,这个函数的不定积分

以下过程我将会说英文,高中生应该具备理解英文的能力噢.
∫lnx/(x²+1)^(3/2) dx
= ∫lnx d[∫dx/(x²+1)^(3/2)] = ∫lnx d[x/√(x²+1)],integration by parts,1st step
= (xlnx)/√(x²+1) - ∫x/√(x²+1) dlnx,integration by parts,2nd step
= ...- ∫x/√(x²+1) * (1/x) dx = ...- ∫dx/√(x²+1)
For the term ∫dx/√(x²+1),let x=tanθ => dx=sec²θ dθ,sinθ=x/√(x²+1),cosθ=1/√(x²+1)
= ...- ∫(sec²θ dθ)/(secθ) = ...- ∫secθ dθ
= ...- ln|secθ+tanθ| + C
= (xlnx)/√(x²+1) - ln|x+√(x²+1)| + C