Integral test

: Math 2730 Sequences and Series: Integral test
   By Anonymous on Monday, February 04, 2008 - 10:48 pm: Edit Post

I was working on the problems from section 12.3 in the text and i got stuck with #18.

So you can use the integral test with #18 since the associated function is decreasing, positive, and continuous. I'm just wondering how to take the integral of 1/(x^2 -4x +5). I feel like this should be really easy but I just can't think of anything...

thanks


   By Sasho on Monday, February 04, 2008 - 11:05 pm: Edit Post

(x^2 - 4x +5)=(x - 2)^2 +1. Now the substitution x - 2 =u will lead you to tan^{-1}(x - 2).


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