Question

1/(3x) 的不定积分是1/3ln(x)+c还是1/3ln(3x)+c?（设x>0)

Answer 1

(1/3)*ln(x)+c1和(1/3)*ln(3x)+c2都是对的!
两个表达式的c1和c2不相等
(1/3)*ln(3x)+c2
=(1/3)*[ln(3)+ln(x)]+c2
=(1/3)*ln(x)+[(1/3)ln(3)+c2)
=(1/3)*ln(x)+c1
c1=c2+(1/3)*ln(3)