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3.6http://trevorcreech.com/blog/2008/07/27/calculus-fun/

Calculus Fun

This pretty much sums up my life right now:
\int \dfrac{x^3}{x^3 + 1} = x - \dfrac{1}{3} ln|x+1| + \dfrac{1}{6} ln|x^2 - x + 1| - \dfrac{1}{\sqrt{3}} \arctan(\dfrac{2x-1}{\sqrt{3}}) + C
On the midterm, we were expected to work this out by hand.

2 Comments

  1. I think the answer is actually 4.

    This tests our understanding of calculus how exactly? I think it is a better test of how performing numerous lines of simple math in your head, under pressure, without making a single mistake. This reminds me of PDeng. Why not test application, or something that truly tests understanding of the material?

    Thursday, October 9, 2008 at 10:59 | Permalink
  2. Joseph wrote:

    Granted, this is an uglier integral, I believe that the understanding of how it evaluates can help with other areas substantially.

    Even in looking up integral forms in the tables will not always be evident, and they require knowledge of the techniques of integration in order to fit a desired integral to a specific solution.

    Sunday, October 12, 2008 at 2:21 | Permalink

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