Obliczamy całkę metodą podstawiania: \[ \begin{split} \int \frac{dx}{\cos^{2\!}{(1-9x)}} &=\begin{vmatrix}t=1-9x \\ dt=-9dx \\-\frac{dt}{9}=dx\end{vmatrix} =\\[6pt] &=\int \frac{-\frac{dt}{9}}{\cos^{2\!}{t}}=\\[6pt] &=-\frac{1}{9}\int \frac{dt}{\cos^{2\!}{t}}=\\[6pt] &=-\frac{1}{9}\operatorname{tg}{t}+C=\\[6pt] &=-\frac{1}{9}\operatorname{tg}(1-9x)+C \end{split} \]