Answer
$\ln |2+\sec y|+c$
Work Step by Step
Solve $\int\dfrac{\sec y \tan y dy}{2+\sec y}$
Let $p=2+\sec y$ and $dp=3 \sec^2 t$
This implies $\int\dfrac{\sec y \tan y dy}{2+\sec y}=\int\dfrac{dp}{p}=\ln|p|+c$
Since, $p=2+\sec y$
Thus, $\int\dfrac{\sec y \tan y dy}{2+\sec y}=\ln |2+\sec y|+c$