Question

高数，不定积分，麻烦一位大神帮我学明白第二类换元法求积分

Answer 1

t=√(x-3),x=t^2+3,dx=2tdt
∫x/√(x-3) dx
=∫(t^2+3)/t*2tdt
=∫(2t^2+3)dt
=2/3*t^3+3t+c
=2/3*(x-3)^(3/2)+3*(x-3)^(1/2)+c
2.
x=sint, t∈（0，π/2),dx=costdt

∫cost*cost/sint dt=∫(1-sintsint)/sint dt=∫1/sint-sint dt
=∫csctdt+cost+c
=

追问

不明白啊