Saturday

January 31, 2015

January 31, 2015

Posted by **Paul** on Saturday, September 15, 2012 at 12:13pm.

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 12:31pmNasty 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 12:45pmalright, thanks Reiny!

- Definite Integral -
**Steve**, Saturday, September 15, 2012 at 11:18pmThe 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 9:39amThanks Steve!

**Answer this Question**

**Related Questions**

math - How do you find the definite integral of an absolute function? ∫_0^...

Definite integral by parts (correction) - Hello, I just wanted to verify if my ...

math - Evaluate definite integral of (2x+2)(x^2 + 2x -5)^5dx upper limit 2 and ...

integral calculus - Evaluate the following intergal:- integral of [Mvdv] with ...

Calculus Fundamental Theorem - Evaluate the definite integral. function: x+13 ...

integral calculus.. - Evaluate the following integral:- Mvdv , with upper ...

math - Evaluate the following integral: Integral lower limit 0 and upper limit 2...

Calculus Area between curves - Evaluate the definite integral: sqrt(8-2x) lower ...

Calculus - Hello, I just wanted to verify if my work was good. Calculate the ...

math - Sorry I posted this question earlier with a error. Can anyone help me ...