# Antiderivative Example

• Nov 8th 2009, 12:39 PM
ty2391
Antiderivative Example
Hello,
I was doing the antiderivative of:

f'(x) = (x^2-1)/x

Am I allowed to separate this into x^2/x - 1/x? Or do the brackets prevent me from doing so?

If not, how do I approach this antiderivative? Thanks for anyone's help!
• Nov 8th 2009, 12:41 PM
skeeter
Quote:

Originally Posted by ty2391
Hello,
I was doing the antiderivative of:

f'(x) = (x^2-1)/x

Am I allowed to separate this into x^2/x - 1/x? Or do the brackets prevent me from doing so?

If not, how do I approach this antiderivative? Thanks for anyone's help!

you have the correct approach ... $\frac{x^2-1}{x} = x - \frac{1}{x}$

antiderivative is $\frac{x^2}{2} - \ln|x| + C$
• Nov 8th 2009, 03:49 PM
ty2391
Quote:

Originally Posted by skeeter
you have the correct approach ... $\frac{x^2-1}{x} = x - \frac{1}{x}$

antiderivative is $\frac{x^2}{2} - \ln|x| + C$

Thanks a lot,

I forgot to mention that f(1) = 1/2, and f(-1) = 0
When I solve for c, I get two different values when x=1 and x=-1.
(C=0 when x=1, C=1/2 when x=-1)

Does this mean C=0 when x>0 and C=1/2 when x<0?
• Nov 8th 2009, 03:58 PM
skeeter
Quote:

Originally Posted by ty2391
Thanks a lot,

I forgot to mention that f(1) = 1/2, and f(-1) = 0
When I solve for c, I get two different values when x=1 and x=-1.
(C=0 when x=1, C=1/2 when x=-1)

Does this mean C=0 when x>0 and C=1/2 when x<0?

looks that way, doesn't it?