basic integration help

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basic integration help derp Fri Jan 20 07:42:52 2012 No.4272705 [Reply] [Original]

Hey guys, I derped and missed the first integration practice of my basic calculus course.

I know how to integrate by parts, but in the homework we are asked to solve the basic integrals without that or substitution, so, I have no idea.

integrate x^2dx/(1+x)

thanks in advance guys!

>>	Anonymous Fri Jan 20 07:43:00 2012 No.4272706 (x) ___ 6xd^2

>>	Anonymous Fri Jan 20 07:47:32 2012 No.4272714 <div class="math">\frac{x^2}{x+1}=\frac{x^2-1+1}{x+1}=\frac{1}{x+1}+x-1</div> Now it is easy as fuck. sometimes you have to be creative, look for workarounds in math!

>>	derp Fri Jan 20 07:55:27 2012 No.4272731 >>4272714 Thanks anon! Really didn't think about the good ol' +1-1 workaround, used it alot in limit calculation and didn't spring to mind here.

derp Fri Jan 20 08:01:08 2012 No.4272745

hmm, right...another quick question: I've reached the previous form and split the integrals, all easy and such, and in the end got

x^2/2-x+ln |x+1| + c

wolfram, however, adds another 3/2 in the end...why is that?

http://www.wolframalpha.com/input/?i=integral+x%5E2dx%2Fx%2B1

>>	Anonymous Fri Jan 20 08:02:08 2012 No.4272747 >>4272731 using the identity is useful all over the place

>>	Anonymous Fri Jan 20 08:08:03 2012 No.4272757 >>4272745 Thats weird but your integral is right because 3/2 is a constant, so take c+3/2 and call it D, another constant

>>	Anonymous Fri Jan 20 08:08:55 2012 No.4272756 >>4272745 doesn't matter, it ends up the C term anyways

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