What is the correct solution for this integral?

[alba_ei]

Homework Statement

\int \frac{ae^\theta+b}{ae^\theta-b} \, d\theta

The Attempt at a Solution

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

\int \frac{u + b + b}{u} \, du

\int du +\int \frac{2b}{u} \, du

= u \du + 2b \ln u +C

= u + 2b \ln u +C

= ae^\theta-b + 2b\ln (ae^\theta-b)

but the answer of the book is
\int \frac{ae^\theta+b}{ae^\theta-b} \, d\theta = 2\ln (ae^\theta-b) - \theta + C
what did i do wrong?

 

[Galileo]

You didn't subsitute properly. You have to change dtheta too.

 

[ziad1985]

write d0 as what it should equal to du
for example if u=x^2
du=2*xdx