Integrating exponentials and trig

The idea

Reverse the standard derivatives: $\int e^{kx}\,dx = \frac{1}{k}e^{kx} + c$, $\int \frac{1}{x}\,dx = \ln|x| + c$, $\int \cos kx\,dx = \frac{1}{k}\sin kx + c$, $\int \sin kx\,dx = -\frac{1}{k}\cos kx + c$ and $\int \sec^2 kx\,dx = \frac{1}{k}\tan kx + c$.

1. Match each term to a standard result.
2. Divide by the coefficient of $x$ inside.
3. Add $+ c$, or apply the limits for a definite integral.

Watch out Integrating $e^{2x}$ gives $\frac{1}{2}e^{2x}$: divide by $2$, do not multiply.