Obliczamy całkę metodą podstawiania: \[ \begin{split} \int 3^{4x-1}dx &=\begin{vmatrix} t=4x-1 \\ dt=4dx \\dx = \frac{1}{4}dt\end{vmatrix}=\\[6pt] &=\int 3^t\cdot \frac{1}{4}dt=\\[6pt] &=\frac{1}{4}\int3^tdt=\\[6pt] &=\frac{1}{4}\cdot \frac{3^t}{\ln 3}+C=\\[6pt] &=\frac{3^{4x-1}}{4\ln 3}+C \end{split} \]