107. $\int \frac{d x}{\cos ^{2}(2 x+1)}$.

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.

107. $\int \frac{d x}{\cos ^{2}(2 x+1)}$.
Solution. Due to the previously made remark, the argument should stand under the differential sign. Since $d(2 x+1)=2 d x$, then $d x=$ $=\frac{1}{2} d(2 x+1)$. Therefore,

$$
\int \frac{d x}{\cos ^{2}(2 x+1)}=\frac{1}{2} \int \frac{d(2 x+1)}{\cos ^{2}(2 x+1)}=\frac{1}{2} \operatorname{tg}(2 x+1)+C
$$