77. $\int \frac{\sin 2 x}{\cos x} d x$.

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77. $\int \frac{\sin 2 x}{\cos x} d x$.
Solution. Applying the formula $\sin 2 x=2 \sin x \cos x$, we get

$$
\int \frac{\sin 2 x}{\cos x} d x=\int \frac{2 \sin x \cos x}{\cos x} d x=2 \int \sin x d x=-2 \cos x+C
$$