Calculus

posted by .

1. Evaluate the following integrals
(a) 􏰀 4x2 +6x−12 / x3 − 4x dx

  • Calculus -

    I will assume you meant
    (4x^2 +6x−12)/(x^3 − 4x)
    = (4x^2 + 6x - 12)/( x(x+2)(x-2) )

    split it into partial fractions

    let
    A/x + B/(x+2) + C/(x-2) = (4x^2 + 6x - 12)/( x(x+2)(x-2) )

    multiply by x(x+2)x-2)

    A(x^2-4) + Bx(x-2) + Cx(x+2) = 4x^2 + 6x - 12

    This must be true for all x's
    let x = 0
    -4A = -12
    A=3
    let x = 2
    8C = 16 + 12-12 = 16
    C = 2
    let x = -2
    8B = 16 + 12-12 = -8
    B = -1

    so ∫ (4x^2 + 6x - 12)/( x(x+2)(x-2) ) dx
    = ∫3/x dx + ∫-1/(x+2)dx + ∫2/(x-2) dx
    = 3ln x - ln(x+2) + 2ln(x-2) + k, where k is a constant

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find an equation for the surface consisting of all points P(x, y, z) equidistant from the point P(0, 1, 0) and the plane x = 3. Answer Choices: 1. y2 + z2 − 6x + 2y − 8 = 0 2. x2 + z2 + 6y − 2z − 8 = 0 3. y2 …
  2. Math

    First, give the technology formula for the given function and then use technology to evaluate the function for the given values of x. (Round your answers to four decimal places.) r(x) = 4x2 + 1/4x2 − 1; x = −1, 0, 1, ..., …
  3. biology

    Given the part of the molecule shown below, can the underlined atom participate in a hydrogen bond with an approriate bonding partner?
  4. Grade 12 Calculus

    Evaluate each of the following. Show all your calculations. a) f'(3) if f(x)  = x^4 − 3x b) f' (−2) if f(x) = 2x^3 + 4x^2 − 5x + 8 c) f" (1) if f(X)  = −3x^2 − 5x + 7 …
  5. calculus (gr 12)

    Evaluate each of the following. Show all your calculations. a) f'(3) if f(x)  = x^4 − 3x b) f' (−2) if f(x) = 2x^3 + 4x^2 − 5x + 8 c) f" (1) if f(X)  = −3x^2 − 5x + 7 …
  6. calculus (gr 12)

    Evaluate each of the following. Show all your calculations. a) f'(3) if f(x)  = x^4 − 3x b) f' (−2) if f(x) = 2x^3 + 4x^2 − 5x + 8 c) f" (1) if f(X)  = −3x^2 − 5x + 7 …
  7. calculus (gr 12)

    Evaluate each of the following. Show all your calculations. f′ (3/4)if f(x) = −3x^3 − 7x^2 + 4x − 11
  8. calculus

    Evaluate each of the following. Show all your calculations. f′ (3/4)if f(x) = −3x^3 − 7x^2 + 4x − 11
  9. calculus

    Evaluate each of the following. Show all your calculations. f" (−3) if f(x)  = 4x^3 − 3x^2 + 2x − 6
  10. precalc

    Find the exact value of each expression, if it exists: the -1 are representing the inverse functions! (a) sin -1 (-√2/2) (b) cos−1 (−1) (c) sin( 􏰀sin−1 (π)􏰁) (d) cos−1􏰀(cos􏰀(−4π􏰁􏰁/ …

More Similar Questions