Question

Show that the function f(x)= integral from x to 3x 1/t ft is constant on the interval (0, positive infinity)

Answer 1

`\int\limits^(3x)_x { (1)/(t) } \, dt`
integrate to get

`[ln|t|]^(3x)_x=ln|3x|-ln|x|=ln| (3x)/(x)| =ln |3|=ln(3)`
this only is true when x>0
when x turns negative, we get -ln(3) because of math