Question

Find: \[ \int \frac{\cos x}{(2+\sin x)(4+\sin x)}\,dx. \]

Hint:

When linear terms in the denominator differ by a constant, you can skip full partial fractions by using the difference observation: \( \frac{1}{(t+2)(t+4)} = \frac{1}{2} \left[ \frac{1}{t+2} - \frac{1}{t+4} \right] \).

Answer 1