Integration of Exponential Functions
Example 1:
$$\int e^{4x} \, dx $$Solution:
- $$\textup{Let}\,\, u=4x$$
- $$du=4dx$$
- $$\frac{du}4=dx$$
- $$\int e^{4x} \, dx = \int e^u\,\, \frac{du}4$$
- $$= \frac{1}4 \int e^u\,du$$
- $$= \frac{1}4 \, e^u+C$$
- $$= \frac{1}4 \, e^{4x}+C$$