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 button-pushing.

- 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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