Partial Fractions Calc Problem

[coookiemonste]

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.

 

[gabbagabbahey]

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)

 

[muso07]

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 ?

 

[HallsofIvy]

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 ?