Posted by **Jenna** on Sunday, December 6, 2009 at 9:59pm.

Express the integrals as the sum of partial fractions and evaluate the integral:

(integral of) (x^2)dx/(x-1)(x^2 +2x+1)

My work:

The above integral is equal to x^2dx/(x+1)^2

(A/x-1) + (B/x+1) + (Cx+D)/(x+1)^2 = x^2

A(x+1)^2 + B(x-1)(x+1) + (Cx+d)(x-1) = x^2

Ax^2 + 2Ax + A + Bx^2 + Cx^2 - Cx -D = x^2

x^2(A+B+C) + x(2A -C+D) + (A-B-D) = x^2

Which gives us the following equations:

A+B+C = 1

2A-C+d= 0

A-B-D=0

The problem is once I get to this point, I get stuck. I'm not sure how to solve for A,B,C, and D.

- calc II -
**MathMate**, Monday, December 7, 2009 at 8:51am
You do not really have a problem.

There are two ways to do a partial fraction with multiple factors in the denominator, and you have combined the two.

For the multiple factor of (x+1)², you could *either* assume

B/(x+1)+D/(x+1)² *or*

(Cx+D)/(x+1)²

In your particular problem, this is the equivalent of setting C=0, and proceed to solve for A,B and D with the three equations that you have correctly set up.

## Answer This Question

## Related Questions

- Calc II - Perform long division on the integrand, write the proper fraction as a...
- calc - find integral using table of integrals ) integral sin^4xdx this the ...
- calculus - evaluate integral or state that it is diverges integral -oo, -2 [2/(x...
- Calc - integral (x^3)/(x^2-2x+1) from -1 to 0 How do you get this integral? I ...
- Calc easy - Having trouble getting the correct solution. The integral of “x ...
- Calc 2 - a. Integral (x^2)/(sqrt(1+(x^2))) Would I separate these two into 2 ...
- calc asap! - can you help me get started on this integral by parts? 4 S sqrt(t) ...
- Quick calc question - If f(x) and g(x) are continuous on [a, b], which one of ...
- calculus - a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write...
- calculus - find the exact length of the curve y = ln(1-x^2), 0 <= x <= (1/...

More Related Questions