177. $\int \sin n x d x$.

177. $\int \sin n x d x$. 

The translation is provided as requested, however, it seems the source text is a mathematical expression which is already in a universal format and does not change in translation. If you need an explanation or solution for the integral, please let me know.
Solution. $\int \sin n x d x=\left|\begin{array}{l}t=n x, \\ d t=n d x, \\ d x=\frac{1}{n} d t\end{array}\right|=\frac{1}{n} \int \sin t d t=-\frac{1}{n} \cos t+C=$ $=-\frac{1}{n} \cos n x+C$.

Therefore,

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