# Definite Integral

posted by .

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 -

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 -

alright, thanks Reiny!

• Definite Integral -

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 -

Thanks Steve!

## Similar Questions

1. ### math

How do you find the definite integral of an absolute function?
2. ### integral calculus..

Evaluate the following integral:- çMvdv , with upper limit 'v' and lower limit 'u'
3. ### integral calculus

Evaluate the following intergal:- integral of [Mvdv] with upper limit 'v' and lower limit 'u'
4. ### Definite integral by parts (correction)

Hello, I just wanted to verify if my work was good. Calculate the following integral by parts: ∫ upper limit is 1/5 and lower limit is 1/10. of 10sin^-1 (5x)dx so first I named the variables: u = 10 sin^-1 (5x) du = 50 / sqr(1-25x^2) …
5. ### Calculus

Hello, I just wanted to verify if my work was good. Calculate the following integral by parts: ∫ upper limit is 1/5 and lower limit is 1/10. of 10sin^-1 (5x)dx so first I named the variables: u = 10 sin^-1 (5x) du = 50 / sqr(1-25x^2) …
6. ### math

Sorry I posted this question earlier with a error. Can anyone help me solve this now?
7. ### math

Evaluate the following integral: Integral lower limit 0 and upper limit 2 of 3x(x-7)dx
8. ### Calculus Fundamental Theorem

Evaluate the definite integral. function: x+13 with respect to variable x lower limit:0 upper limit:22