1/(1+根号下1-3x)的不定积分

Question

1/(1+根号下1-3x)的不定积分

Answer 1

∫1/[1+√(1-3x)]dx
设1-3x=t^2,x=(1-t^2)/3,dx=-2/3tdt
=∫1/(1+t)*-2/3tdt
=-2/3∫dt+∫1/(1+t)dt
=-2/3t+2/3ln|1+t|+C
=-2/3√(1-3x)+2/3ln|1+√(1-3x)|+C
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