Answer
$2.5\ln|2+e^{1.2x}|+C$
Work Step by Step
$I=\displaystyle \int\frac{3e^{1.2\kappa}}{2+e^{1.2x}}dx=\int\frac{1}{2+e^{1.2x}}(3e^{1.2\kappa}dx)$
Substitute: $\left[\begin{array}{llll}
u & =2+e^{1.2x} & & \\
& & & \\
du & =1.2e^{1.2x}dx & \Rightarrow & 3e^{1.2x}dx=\dfrac{3du}{1.2}
\end{array}\right]$
$I=\displaystyle \int\frac{1}{u}\cdot\frac{3du}{1.2}=\frac{3}{1.2}\int\frac{du}{u}$
$=2.5\displaystyle \int u^{-1}du$
special case of the power rule $(n=-1)$
$=2.5\ln|u|+C$
bring back the variable $x$
= $2.5\ln|2+e^{1.2x}|+C$
