Common Integration Formulas Dataset
This dataset provides a comprehensive list of 56 common integration formulas, detailing functions, their integrals, conditions, and notes. Ideal for students, educators, and professionals in mathematics.
📥 Free Download
💡 Key Takeaways
- Access 56 essential integration formulas for calculus.
- Explore categories like basic, trigonometric, and exponential functions.
- Download ready-to-use formulas with conditions and notes.
- Leverage accurate integral definitions for educational or professional use.
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Showing 20
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⚠️ Showing first 20 of 56 records. Download the file for complete data.
| Category | Function f(x) | ∫f(x)dx | Condition | Notes |
|---|---|---|---|---|
| Basic | k | kx + C | k is constant | Constant rule |
| Basic | x^n | x^(n+1)/(n+1) + C | n ≠ -1 | Power rule |
| Basic | 1/x | ln|x| + C | x ≠ 0 | Natural logarithm |
| Basic | e^x | e^x + C | - | Exponential function |
| Basic | a^x | a^x/ln(a) + C | a > 0, a ≠ 1 | General exponential |
| Basic | x^(-1/2) | 2√x + C | x > 0 | Square root form |
| Trigonometric | sin(x) | -cos(x) + C | - | Sine function |
| Trigonometric | cos(x) | sin(x) + C | - | Cosine function |
| Trigonometric | tan(x) | -ln|cos(x)| + C | x ≠ π/2 + nπ | Tangent function |
| Trigonometric | cot(x) | ln|sin(x)| + C | x ≠ nπ | Cotangent function |
| Trigonometric | sec(x) | ln|sec(x) + tan(x)| + C | x ≠ π/2 + nπ | Secant function |
| Trigonometric | csc(x) | ln|csc(x) - cot(x)| + C | x ≠ nπ | Cosecant function |
| Trigonometric | sec²(x) | tan(x) + C | x ≠ π/2 + nπ | Secant squared |
| Trigonometric | csc²(x) | -cot(x) + C | x ≠ nπ | Cosecant squared |
| Trigonometric | sec(x)tan(x) | sec(x) + C | x ≠ π/2 + nπ | Product form |
| Trigonometric | csc(x)cot(x) | -csc(x) + C | x ≠ nπ | Product form |
| Trigonometric | sin²(x) | x/2 - sin(2x)/4 + C | - | Half-angle identity |
| Trigonometric | cos²(x) | x/2 + sin(2x)/4 + C | - | Half-angle identity |
| Inverse Trig | 1/√(1-x²) | arcsin(x) + C | |x| < 1 | Arcsine form |
| Inverse Trig | -1/√(1-x²) | arccos(x) + C | |x| < 1 | Arccosine form |
🔧 Use Cases
- Import the CSV file into your Python script or SQL database to build custom calculus solvers or educational tools.
- Use the Excel file to filter formulas by category, create study guides, or verify calculations for complex problems.
- Print the PDF version for a quick reference guide in classrooms, during exams, or for offline study sessions.
- Integrate this dataset into e-learning platforms to provide a structured resource for students learning integral calculus.