Summary of Integrals Involving Exponential and Logarithmic Functions
Essential Concepts
- Exponential and logarithmic functions arise in many real-world applications, especially those involving growth and decay.
- Substitution is often used to evaluate integrals involving exponential functions or logarithms.
Key Equations
- Integrals of Exponential Functions
[latex]\displaystyle\int {e}^{x}dx={e}^{x}+C[/latex]
[latex]\displaystyle\int {a}^{x}dx=\frac{{a}^{x}}{\text{ln}a}+C[/latex]
- Integration Formulas Involving Logarithmic Functions
[latex]\displaystyle\int {x}^{-1}dx=\text{ln}|x|+C[/latex]
[latex]\displaystyle\int \text{ln}xdx=x\text{ln}x-x+C=x(\text{ln}x-1)+C[/latex]
[latex]\displaystyle\int {\text{log}}_{a}xdx=\frac{x}{\text{ln}a}(\text{ln}x-1)+C[/latex]
