12 Multiple Choice 1 point Do not integrate, but state which method(s) can be used to evaluate the integral: \( \int(x+1) /\left(x^{2}+2 x-8\right) d x \)

We start by factoring the denominator: x² + 2x – 8 = (x – 2)(x + 4). Now, notice that the derivative of x² + 2x – 8 is 2x + 2, which equals 2(x + 1). Since the numerator is x + 1, you can rewrite the integrand as   ½ · [2(x + 1)]/(x² + 2x – 8). This observation shows that if you let u = x² + 2x – 8, then du = 2(x + 1) dx, making the substitution method perfectly applicable. Alternatively, since the integrand, after factoring the denominator, becomes a rational function with linear factors in the denominator, partial fractions can be used. Thus, the methods that can be used to evaluate the integral are either u-substitution or partial fraction decomposition.