functions
Calculus
Integration Rules Cheat Sheet
Complete integration rules cheat sheet with all antiderivative formulas, substitution, integration by parts, and trigonometric integrals. Free PDF download.
Basic Integration Rules
| Name | Formula | Notes |
|---|---|---|
| Constant | ||
| Power Rule | Valid for n ≠ -1. Add 1 to exponent, divide by new exponent | |
| Sum Rule | ||
| Constant Multiple |
Common Integrals
| Name | Formula | Notes |
|---|---|---|
| 1/x | ||
| Exponential | ||
| General Exponential |
Trigonometric Integrals
| Name | Formula | Notes |
|---|---|---|
| Sine | ||
| Cosine | ||
| Secant Squared | ||
| Cosecant Squared | ||
| Secant Tangent | ||
| Cosecant Cotangent | ||
| Tangent | ||
| Secant |
Inverse Trig Integrals
| Name | Formula | Notes |
|---|---|---|
| Arcsine Form | ||
| Arctangent Form |
Integration Techniques
| Name | Formula | Notes |
|---|---|---|
| U-Substitution | Let u = g(x), then du = g'(x)dx | |
| Integration by Parts | Choose u and dv wisely (LIATE rule) |
Definite Integrals
| Name | Formula | Notes |
|---|---|---|
| Fundamental Theorem | Where F'(x) = f(x) | |
| Area Between Curves | Top minus bottom |
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