Posted by Paul on Saturday, September 15, 2012 at 12:13pm.
Nasty integral
long division will get you nowhere.
It would have been a good idea if the fraction had been flipped
If the denominator would have factored we could have used "integration by partial fractions" , but no such luck ( x^2 + 4x + 7 has no real roots, so we can't form real factors)
I tried integration by parts and bailed out after a messy start, and went to good ol' reliable
WOLFRAM
http://integrals.wolfram.com/index.jsp?expr=%285x%2B3%29%2F+%28x%5E2+%2B+4x+%2B+7%29&random=false
(when they say log, they actually imply Ln )
now sub in the upper and lower values and good luck on the button-pushing.
alright, thanks Reiny!
The way to get their answer is to complete the square and then use trig substitution.
If you go to wolframalpha.com and type in
∫ (5x + 3) / (x^2 + 4x + 7) dx
then click the "Show Steps" button you can see how they did it. If you want the final numeric answer, type in
∫[-2,1] (5x + 3) / (x^2 + 4x + 7) dx
to get log32 - 7pi/sqrt(27)
Thanks Steve!
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