178. $\int \cos n x d x$.

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178. $\int \cos n x d x$.
Solution. $\int \cos n x d x=\left|\begin{array}{l}t=n x, \\ d t=n d x, \\ d x=\frac{1}{n} d t\end{array}\right|=\frac{1}{n} \int \cos t d t=\frac{1}{n} \sin t+C=$ $=\frac{1}{n} \sin \pi x+C$.

Therefore,

$$
\int \cos n x d x=\frac{1}{n} \sin n x+C
$$

It is useful to remember formulas (1) and (2) and use them as table integrals.