Posted by Maryam on Sunday, May 26, 2013 at 3:33am.
1. Evaluate the following integrals
(a) 4x2 +6x−12 / x3 − 4x dx

Calculus  Reiny, Sunday, May 26, 2013 at 7:48am
I will assume you meant
(4x^2 +6x−12)/(x^3 − 4x)
= (4x^2 + 6x  12)/( x(x+2)(x2) )
split it into partial fractions
let
A/x + B/(x+2) + C/(x2) = (4x^2 + 6x  12)/( x(x+2)(x2) )
multiply by x(x+2)x2)
A(x^24) + Bx(x2) + 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 + 1212 = 16
C = 2
let x = 2
8B = 16 + 1212 = 8
B = 1
so ∫ (4x^2 + 6x  12)/( x(x+2)(x2) ) dx
= ∫3/x dx + ∫1/(x+2)dx + ∫2/(x2) dx
= 3ln x  ln(x+2) + 2ln(x2) + k, where k is a constant
Answer This Question
Related Questions
 Grade 12 Calculus  Evaluate each of the following. Show all your calculations. ...
 precalc  Find the exact value of each expression, if it exists: the 1 are ...
 calculus (gr 12)  Evaluate each of the following. Show all your calculations. a...
 calculus (gr 12)  Evaluate each of the following. Show all your calculations. a...
 Math  First, give the technology formula for the given function and then use ...
 biology  Given the part of the molecule shown below, can the underlined atom ...
 calculus  Find an equation for the surface consisting of all points P(x, y, z) ...
 calculus  Evaluate each of the following. Show all your calculations. f′...
 calculus (gr 12)  Evaluate each of the following. Show all your calculations. f...
 calculus  Evaluate each of the following. Show all your calculations. f...
More Related Questions