(1) \( 1/x \) equations
$$\int \frac{1}{x} \, dx = \ln |x|$$
$$\int \frac{1}{ax+b} \, dx = \frac{1}{a} \ln |ax+b|$$
(2) \( e \) equations
$$\int e^x \, dx = e^x$$
$$\int e^{ax+b} \, dx = \frac{1}{a} e^{ax+b}$$
(3) Trigonometry
$$\begin{array}{|c|c|}\hline \sin x, \sin(ax+b) & - \cos x, -\frac{1}{a}\cos(ax+b)\\ \hline \cos x, \cos(ax+b) & \sin x, \frac{1}{a}\sin(ax+b)\\ \hline \sec x, \sec(ax+b) & \tan x, \frac{1}{a}\tan(ax+b) \\ \hline \end{array}$$