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Title: Why do you need absolute value signs when an integral of something is a natural log? Post by: ijk90825 on Sep 23, 2012 For example:
[integral of 1/(x+5)] = ln|x+5| I know you don't always put the absolute value signs there, so how do you know when you need them? And Isn't that going to mess with your answer? Title: Why do you need absolute value signs when an integral of something is a natural log? Post by: datty117 on Sep 23, 2012 Well think about it you can't take the Ln of any negative number unless your working with complex numbers. So the Absolute value is just there to turn the negative into positive.
Example Ln|-10| would be correct But Ln(-10) would be a non-existent solution Title: Why do you need absolute value signs when an integral of something is a natural log? Post by: davashkai on Sep 23, 2012 The ln function is only defined when its argument is positive. (In your case the argument is x+5). And to ensure that an argument is positive, we sometimes need to put absolute value signs around it.
Eg: x+5 can be negative (when x<5), so we need ln|x+5| not ln(x+5) But x^2 +1 is always positive, so ln(x^2+1) is fine Also, ln is not defined when its argument is zero. So I suppose technically for your integral your answer should be "ln|x+5| + constant, where x cannot equal -5", however, simply "ln|x+5| + constant" is generally written. |