(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int \frac{ae^\theta+b}{ae^\theta-b} \, d\theta[/tex]

3. The attempt at a solution

i took [tex]u = ae^\theta-b[/tex] so [tex]e^\theta = \frac{u + b}{a}[/tex] then i substituded back into the integral and iget this

[tex]\int \frac{u + b + b}{u} \, du[/tex]

[tex]\int du +\int \frac{2b}{u} \, du[/tex]

[tex]= u \du + 2b \ln u +C[/tex]

[tex]= u + 2b \ln u +C[/tex]

[tex]= ae^\theta-b + 2b\ln (ae^\theta-b) [/tex]

but the answer of the book is

[tex]\int \frac{ae^\theta+b}{ae^\theta-b} \, d\theta = 2\ln (ae^\theta-b) - \theta + C [/tex]

what did i do wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question about this integral

**Physics Forums | Science Articles, Homework Help, Discussion**