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integration using partial fractions

  • 28-04-2008 2:35am
    #1
    subzero12
    Closed Accounts Posts: 96 ✭✭


    i need help trying to work out these questions i really dont get them at the minute the examples i was given where
    thanks for any help in advance .
    (1)
    5x/((x-1)(x+3))
    (2)
    3/2x^2+7x+3


Comments

  • #2
    LeixlipRed
    Closed Accounts Posts: 6,081 ✭✭✭LeixlipRed


    The idea here is to break the fraction you are given into seperate fractions which it is easy to integrate using substitution. So number (1) can be broken up into two fractions:

    A/(x-1) + B/(x+3)

    You then turn this back into one fraction which of course is equal to what you originally had and compare coefficients to solve for A and B.

    In number (2) you will do something similar but first you must factorise2x^2 + 7x + 3


  • #3
    Fremen
    Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    In particular, in leixlip's example, you need to solve two simultaneous equations in A and B

    We need

    B(x - 1) + A(x + 3) = 5x + 0

    Equate the constants on the left to the constants on the right, and the x's on the left to x's on the right

    3A - B = 0
    B + A = 5 (dividing out an x)


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