Posted by Paul on Saturday, September 15, 2012 at 12:13pm.
Calculate the following integral:
upper limit: 1
lower limit: 2
∫ (5x + 3) / (x^2 + 4x + 7) dx
Do I do a polynomial division for this one?
Thank you

Definite Integral  Reiny, Saturday, September 15, 2012 at 12:31pm
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 buttonpushing.

Definite Integral  Paul, Saturday, September 15, 2012 at 12:45pm
alright, thanks Reiny!

Definite Integral  Steve, Saturday, September 15, 2012 at 11:18pm
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)

Definite Integral  Paul, Sunday, September 16, 2012 at 9:39am
Thanks Steve!
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