Simplifying Integration: A Common Question Answered

[majin_andrew]

This isn't a homework question, just something I was wondering about, and this seemed like the most appropriate place to post it because of its simplicity.

When integrating a function of the form f(x)=(x-a)^{n}, I find I get a different result if I expand the brackets first and then integrate.

Example:
\int2(x-5)dx = (x-5)^{2} + C = x^{2}-10x-25 + C
\int2x-10dx = x^{2}-10x + C

I was wondering if the C in the first equation will simply just be 25 greater than the C in the second equation, or is there more to it than that?

Thanks for your time,
Andrew

 

[rock.freak667]

In your two integrals, the values of 'C' are different. In the first one you have -25 + C, which is in itself another constant k. So you can rewrite it as x² -10x+k. Which is in the same form as your second integral.

 

[majin_andrew]

Thanks rock.freak667!