Integrating Partial Fractions with a Twist: (x + 3) vs (x - 3)

[maxim07]

Homework Statement

Question states that integral of given partial fraction is supposed to equal ln(2/sqrt(3)), but I have tried it and it does not seem to. I believe I have integrated correctly, but maybe it can be simplified in such a way to become ln(2/sqrt(2))

Relevant Equations

Partial fraction to integrate = 5/7(2x+1) + 1/7(x-3)

 

[PeroK]

What happened to the term with $\frac 1 {x - 3}$?

Are you sure there isn't an earlier mistake that led to those fractions?

 

[maxim07]

This is how I go the reactions -pretty sure it’s right

 

[PeroK]

The second term is problem with those limits of integration - in particular at $x = 3$. You can't make that go away.

 

[maxim07]

the denominator of your second integral is (x + 3) not (x - 3) as in the question. The version with (x + 3) is closer to ln(2/sqrt(3) but still differs by about 2.4 x 10^-3.

using (x - 3) does not work since using the limits given the term becomes ln|-1| and ln(0) so maybe there is something wrong with the question