Final answer:
To evaluate the given integral, we can simplify the expression and use the substitution method to solve it.
Step-by-step explanation:
To evaluate the integral ∫ 3sec(θ)tan(θ)/(sec²(θ)−sec(θ)) dθ, we can simplify the expression by factoring out sec(θ) from the numerator. This gives us ∫ 3tan(θ) dθ. Next, we can rewrite tan(θ) as sin(θ)/cos(θ), giving us ∫ 3sin(θ)/cos(θ) dθ. To solve this integral, we can use the substitution method. Let u = cos(θ), then du = -sin(θ) dθ. Making the substitution, the integral becomes ∫ -3 du. Integrating, we get -3u + C, where C is the constant of integration. Finally, substituting u back in terms of θ, we have -3cos(θ) + C as the final answer.