Integrals resulting in Logarithms (1 Viewer)

[ADrew]

With integrals resulting in logarithmic functions, when should it be necessary to use absolute values? EG: integrating 1/x = ln IxI or lnx ?

 

[K4M1N3]

when the resulting function of x is linear. This is because of logarithmic domain (f(x) > 0)
eg. ln|2x-1| not ln(2x-1).....but you can have ln(x^2 + 1) because it is quadratic, and is positive for all x.

 

[ADrew]

Okay thanks.

 

[Drongoski]

No. You should use the |xxxx| for all arguments of the log. If the expression within the absolute value bars is always positive, then the |....| is redundant. But that applies to all arguments whether or not it is a LINEAR FUNCTION. So to be safe always put the argument (i.e. the expression for the log) within the absolute value bars.

Basically logs must have positive arguments.

 

[ADrew]

Even for functions such as ln sinx etc?

 

[seanieg89]

yes