The problem involves evaluating the integral ∫1/[(x+a)(x+b)]dx using partial fractions. The original poster presents an expression for the integral and attempts to decompose the fraction into simpler components.
Participants are actively engaging with the problem, with some providing guidance on the integral of 1/x and the implications of the relationship between A and B. There is a recognition of the need to clarify the values of A and B, but no consensus has been reached on the next steps.
There is an emphasis on the lack of numerical values for A and B, leading to discussions about their relationships rather than specific solutions. Participants are also considering the implications of the equation 1 = B(a-b) in their reasoning.
coookiemonste said: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.
The equation 1= B(a-b) settles that.muso07 said: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 ?