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Partial Fractions Calc Problem

  • #1

Homework Statement


∫1/[(x+a)(x+b)]dx
answer is 1/(a-b) ln[(x+b)/(x+a)] + C


Homework Equations





The Attempt at a Solution



1=A/(x+a) + B/(x+b)
1=B(x+a) + A(x+b)
1=Bx+ Ba + Ax +Ab

so 0=Bx+ Ax, 1=Ba+Ab
A=-B, 1=B(a-b)

∫-1/(x+a) +∫1/(x+b)

Im not sure if I am headed in the right direction or not.
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6

The Attempt at a Solution



1=A/(x+a) + B/(x+b)
This line should really be 1/((x+a)(x+b))=A/(x+a) + B/(x+b)

1=B(x+a) + A(x+b)
1=Bx+ Ba + Ax +Ab

so 0=Bx+ Ax, 1=Ba+Ab
A=-B, 1=B(a-b)
Good, so B=___?

∫-1/(x+a) +∫1/(x+b)

Im not sure if I am headed in the right direction or not.
This should be B∫-1/(x+a) +B∫1/(x+b)
 
  • #3
54
0
How do you know what A and B equal? You don't know numerical values, just what they're equal to in relation to one another.

gabbagabbahey is right, you should get B∫-1/(x+a) +B∫1/(x+b)

Now what do you know about the integral of 1/x ?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,793
922
How do you know what A and B equal? You don't know numerical values, just what they're equal to in relation to one another.
The equation 1= B(a-b) settles that.

gabbagabbahey is right, you should get B∫-1/(x+a) +B∫1/(x+b)

Now what do you know about the integral of 1/x ?
 

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