Partial fractions for (2x^2 + X) / ((x + 1)(X^2 + 1))

[sunny1324]

integral of (2x^2+X) / ( (x+1)(X^2+1) )

(2x^2+X) / ( (x+1)(X^2+1) ) = A/(x+1) + B/(X^2+1)
=A(X^2)+B(X+1)
=AX^2+A+BX+B
X^2(A) + X(B) + (A+B)
A=2
B=1

What did I do wrong? Help please

 

[skeeter]

Re: Partial fractions

integral of (2x^2+X) / ( (x+1)(X^2+1) )

(2x^2+X) / ( (x+1)(X^2+1) ) = A/(x+1) + B/(X^2+1) right side should be ... = A/(x+1) + (Bx+C)/(x^2+1)

 

[sunny1324]

(2x^2+X) / ( (x+1)(X^2+1) ) = A/(x+1) + (BX+C)/(X^2+1)
=A(X^2+1)+(BX+C)(X+1)
=AX^2+A+BX^2+BX+CX+C
=X^2(A+B) +X(B+C)+(A+C)
A+B=2
B+C=1
A+C=0

A=1/2
B=3/2
C=-1/2


so then it's the integral of 1/2 1/(X+1) + [(3/2)X-1/2]/(X^2+1)

is that right so far?

 

[Deleted member 4993]

...A=1/2
B=3/2
C=-1/2

so then it's the integral of 1/2 1/(X+1) + [(3/2)X-1/2]/(X^2+1) <<<< Looks good

 

[DR._Glockman]

TI - 89.

expand(F2-3). ( (2x^2+x)/((x+1)*(x^2+1)),x) = 3x/2(x^2+1) - 1/2(x^2+1) + 1/2(x+1), then integrate.

 

[stapel]

TI - 89.

Okay, so you have a software package you can use to do the algebra for you. But how does that help a student who needs to learn the algebra and to show his/her work in order to receive credit? :shock:

Eliz.

 

[DR._Glockman]

Anyone with a minimum of intellect can do partial fractions. Once they accompolish this feat, modern technology has taken the drudgery out of having to do this manually and is readily available, unless one perfers to do the grunt work.

 

[galactus]

Anyone with a minimum of intellect can do partial fractions. Once they accompolish this feat, modern technology has taken the drudgery out of having to do this manually and is readily available, unless one perfers to do the grunt work.

This is also pka's feeling on the matter. I tend to agree.

 

[Deleted member 4993]

This is also pka's feeling on the matter. I tend to agree.

I tend to disagree...

Football players are asked to do the grunt work in the gym - lift weights, do push-ups - apparently useless workouts (you can use cranes - modern technology - to lift the weights). But we all know that those excercizes (and spinach) develope "muskels".

So - even though we have calculators we still ask second graders to multiply/divide without using calculators...