1. **Stating the problem:** Evaluate the integral $$\int \frac{t^{y^2} + 1}{t^{y^2} - 1} \, dz$$. 2. **Observing the integral:** The integrand is expressed in terms of $t$ and $y$, but the variable of integration is $z$. Since the integrand does not depend on $z$, it is treated as a constant with respect to $z$. 3. **Formula used:** For any constant $C$, $$\int C \, dz = Cz + C_1,$$ where $C_1$ is the constant of integration. 4. **Applying the formula:** Here, $$C = \frac{t^{y^2} + 1}{t^{y^2} - 1}.$$ Thus, $$\int \frac{t^{y^2} + 1}{t^{y^2} - 1} \, dz = \frac{t^{y^2} + 1}{t^{y^2} - 1} z + C_1.$$ 5. **Explanation:** Since the integrand does not depend on $z$, integrating with respect to $z$ simply multiplies the integrand by $z$ and adds the constant of integration. **Final answer:** $$\int \frac{t^{y^2} + 1}{t^{y^2} - 1} \, dz = \frac{t^{y^2} + 1}{t^{y^2} - 1} z + C.$$