Integral Calculus
Integration Formulas:
| Formula | Description |
|---|---|
| Power rule | |
| Logarithmic rule | $$\int \frac{1}{x} dx = \ln |
| Exponential rule | |
| Trigonometric rule | |
| - |
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| - |
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| - $$\int \tan x dx = \ln | \sec x |
| - $$\int \csc x dx = -\ln | \csc x + \cot x |
| - $$\int \sec x dx = \ln | \sec x + \tan x |
| Integration by partials | |
| Partial fractions | Used for integrating rational functions. |
| Improper integrals | Integrals that do not converge absolutely. |
| Beta function | |
| Gamma function | |
| Riemann integral | Provides a rigorous definition of the integral. |
| Definite integrals | Integrals with both upper and lower limits of integration. |
| Integration techniques | |
| - U-substitution | Substituting a new variable |
| - Integration by trigonometric substitution | Using trigonometric identities to simplify the integral. |
| - Integration by rationalization | Rewriting the integrand so that the denominator can be factored into a product of linear factors. |
| - Integration by tabular methods | Using a table of integrals to find the value of the integral. |
