Post a New Question

calc II

posted by .

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 -

    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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc easy

    Having trouble getting the correct solution. The integral of “x squared” in the numerator and “x squared plus x minus 6” in the denominator. S X2 / (X2 + x – 6) dx Thanks! That's a messy one. According to my table of integrals. …
  2. calc asap!

    can you help me get started on this integral by parts?
  3. calculus

    evaluate integral or state that it is diverges integral -oo, -2 [2/(x^2-1)] dx ----------------------------------- integral -oo, -2 [2/(x^2-1)] dx Through partial fractions, I came up with lim [ln(x-1)-ln(x+1)] b, -2 b->-oo I get …
  4. Calc II

    Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and evaluate the integral: (integral of) 2y^4dy/y^3 - y^2 + y - 1 After long divison I get: (integral of)2ydy + 2(integral of)dy + (integral …
  5. calc

    find integral using table of integrals ) integral sin^4xdx this the formula i used integral sin^n xdx =-1/n sin^n-1xcosx +n-1/n integral sin^n-2 using the formula this is what i got: integral sin^4xdx=-1/4sin^3xcosx+3/4 integral sin^2xdx= …
  6. Calc

    integral (x^3)/(x^2-2x+1) from -1 to 0 How do you get this integral?
  7. Calc 2

    a. Integral (x^2)/(sqrt(1+(x^2))) Would I separate these two into 2 separate integrals?
  8. Quick calc question

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is false?
  9. Math

    Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: integral[4,1] …
  10. Calculus II

    Express the integrated as a sum of partial fractions and evaluate the integral 3x2+x+9/(x2+5)(x-6)

More Similar Questions

Post a New Question