2006-06-23 08:59:59 · 8 answers · asked by schenker 1 in Science & Mathematics ➔ Mathematics
You cannot rewrite like this: F(x)=x^-1 becaus the integral of x^a =
x^(a+1)/(a+1) if a is different of -1.
Integral of (1/x) is Ln (|x|) like other people said.
But why?
When the matematicians studied the proprieties of this integral, they discovered that this integral had the same proprieties of the ordinary Log(x).
2006-06-23 09:21:23 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The antiderivative of 1/x is ln|x| + C
This is just one of those things that you need to memorize. There is actually a way to prove that the integral has the logarythmic property (that ln(a*b) = ln(a)+ln(b)) using u-substitutions. But trust me -- it is better to just memorize it.
2006-06-23 16:52:07 · answer #2 · answered by Ranto 7 · 0⤊ 0⤋
the integration of 1/x is ln|x| + C, where C is a constant.
you can verify it by differentiating ln|x| + C
2006-06-23 17:34:49 · answer #3 · answered by canzoni 3 · 0⤊ 0⤋
The answer is log to the base e x. e = exponential. Can also be written as Inx
2006-06-23 16:06:16 · answer #4 · answered by Numptyhead 2 · 0⤊ 0⤋
Rewrite it as x^-1 and do it the way your teacher taught you the first week of class.
2006-06-23 16:02:32 · answer #5 · answered by Rocket Scientist X 2 · 0⤊ 0⤋
It is usually in the inside cover of your book. that is a typical one that you will have to have memorized.
2006-06-23 16:16:30 · answer #6 · answered by ferronferron 2 · 0⤊ 0⤋
the answer is ln(absolute value of(x ))
this is just a calc property
2006-06-23 16:12:05 · answer #7 · answered by dhaval70 2 · 0⤊ 0⤋
i hate math..
2006-06-23 16:03:20 · answer #8 · answered by Anonymous · 0⤊ 0⤋