If $\int \frac{\cos 6x + \cos 9x}{1 - 2 \cos 5x} dx = -\frac{\sin 4x}{k} - \sin x + C$ , t…

The key is to recognize that the numerator can be factored using sum-to-product formulas, and that this factorization will share a common factor with the denominator. Once you simplify by canceling, you'll get a much simpler integrand—likely a sum of basic trig functions. Match your result to the given answer form to find $k$.

The key is to recognize that the numerator can be factored using sum-to-product formulas, and that this factorization will share a common factor with the denominator. Once you simplify by canceling, you'll get a much simpler integrand—likely a sum of basic trig functions. Match your result to the given answer form to find $k$.