Multiple Choice 1 point Do not integrate, but state which method(s) can be used to evaluate the integral: \( \int(x+1) /\left(x^{2}+2 x-8\right) d x \) I. Substitution where \( u=x^{2}+2 x-8 \) II. Partial fractions II. Trig substitution I and II only I only III only II only

To evaluate the integral \[ \int \frac{x+1}{x^{2}+2x-8} \, dx, \] let's analyze the methods listed: 1. **Substitution where \( u = x^{2} + 2x - 8 \)**: This method is applicable because we can differentiate \( u \) to find \( du \) and express \( dx \) in terms of \( du \). The integral can be transformed into a simpler form using this substitution. 2. **Partial fractions**: This method can also be used here. The denominator \( x^{2} + 2x - 8 \) can be factored, and then the integrand can be expressed as a sum of simpler fractions, which can be integrated separately. 3. **Trig substitution**: This method is generally used for integrals involving square roots or specific forms that can be transformed into trigonometric identities. In this case, it does not apply since the integral does not have a suitable form for trigonometric substitution. Based on this analysis, the applicable methods are: - I. Substitution where \( u = x^{2} + 2x - 8 \) - II. Partial fractions Thus, the correct answer is: **I and II only**.