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]