Posted by kchik on Tuesday, December 4, 2012 at 12:47pm.
INTEGRATION USING PARTIAL FRACTIONS
a) 4x^23x+2 / x^3x^22x dx
b) x^2 / (x+1)(x+1)^2 dx
c) 33x / 2x^2+6x dx
d) x^2+2x1 / (x^2+1)(x1) dx
##anybody can help me for this question?

calculus  Steve, Tuesday, December 4, 2012 at 2:41pm
I assume you have trouble doing the partial fractions, not the integration?
x^3x^22x = x(x2)(x+1)
so, what you are looking for is a combination of fractions
A/x + B/(x2) + C/(x+1) which when placed over a common denominator of (x^3x^22x) make a numerator of (4x^23x+2).
To add those simpler fractions, you have a numerator of
A[(x2)(x+1)]+B[(x(x+1)]+C[x(x2)]
= Ax^22Ax2A
+ Bx^2+Bx
+ Cx^22Cx
= (A+B+C)x^2 + (2A+B2C)x + (2A)
for that to be identical to 4x^23x+2, you need
A+B+C = 4
2A+B2C = 3
2A = 2
or, A = 1, B=3, C=2
so you have 1/x + 3/(x2) + 2/(x+1)
integrate that to get some logs.
do the other likewise. Note:
quadratic factors below require (Ax+B) above
repeated factors below require all powers. e.g. */(x+1)^2 > A/(x+1) + B/(x+1)^2, though some numerators may turn out to be zero.
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