不定积分求答案和详细过程

Question

如图 不清楚的那个是3√x

Answer 1

解：令√x=t, x=t^2, dx=2dt;
∫dx/[(1+3√x)√x]=∫2tdt/[t(1+3√x)]=2∫[1/(1+3t)]*(1/3)d(1+3t)=(2/3)ln|1+3t|+C
=(2/3)ln(1+3√x)+C。追问

2∫[1/(1+3t)]*(1/3)d(1+3t) 这一步是怎么凑的微分？

追答

2∫[1/(1+3t)]*(1/3)d(1+3t) =2∫[1/(1+3t)]dt。