Doing a U-substitution on the first one we let U = x - 1 ==> dU = dx.

Find the integral of 3/((x-1)(x+2)) dx from 2 to 3.

Answer: ln(8/5)

I did partial fractions and got when x=-2, B=-1. And when x=1, A=1. What do I do next? Please show all your work.

Tutors, sign in to answer this question.

3/((x-1)(x+2)) = A/(x-1) + B/(x+2) for some numbers A and B.

Simplify both sides of the equation by multiplying by (x-1)(x+2) [we can assume x not equal to 1 and -2].

We thus get

3 = A(x+2) + B(x-1)

Plug in x = -2 to get 3 = -3B ==> B = -1.

Plug in x = 1 to get 3 = 3A ==> A = 1.

Thus INT[3/((x-1)(x+2))]dx = INT[1/(x-1) - 1/(x+2)]dx =

INT[1/(x-1)]dx + INT[-1/(x+2)]dx.

Doing a U-substitution on the first one we let U = x - 1 ==> dU = dx.

Doing a U-substitution on the first one we let U = x - 1 ==> dU = dx.

Doing a V-substituion on the second one we let V = x + 2 ==> dV = dx.

Hence INT[1/(x-1)]dx + INT[-1/(x+2)]dx = INT[1/U]dU - INT[1/V]dV =

ln|U| - ln|V| since INT[1/x]dx = ln|x|.

Hence the Indefinite integral is

ln|x-1| - ln|x+2| + C for some C in the real numbers.

Now integrating from 2 to 3 should yield you ln(8/5).

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Brenda G.

Licensed Middle, High School teacher & CRLA certified Math Tutor

$12.50 per 15 min

View Profile >

Carla A.

Get help with Math! ACT and SAT prep, high school, and college!

$9.75 per 15 min

View Profile >

Cliff W.

Experienced educator/tutor in English,Humanities, ACT, Math, Science

$11.25 per 15 min

View Profile >

## Comments