Evaluate the integral. (use c for the constant of integration.) x2 − 3x + 12 (x2 − 4x + 11)2 dx

If the integrand is

then the easiest way to compute this is to expand the product completely, then integrate the resulting polynomial.

If instead it's

you can split the integrand into partial fractions

On the right side, we have

so that

Then

In both denominators, we can complete the square to write

Then substitute

We have

Since

and

all the remaining integrals are trivial; we end up with

Reverse the substitution:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)