Table of Integrals
Antiderivatives of the basic functions: a table of indefinite integrals.
| f(x) | ∫ f(x) dx |
|---|---|
| 0 | C |
| 1 | x + C |
| xn, n ≠ −1 | xn+1 / (n + 1) + C |
| 1/x | ln |x| + C |
| ex | ex + C |
| ax | ax / ln a + C |
| sin x | −cos x + C |
| cos x | sin x + C |
| 1 / cos²x | tan x + C |
| 1 / sin²x | −cot x + C |
| 1 / √(1 − x²) | arcsin x + C |
| 1 / (1 + x²) | arctan x + C |
An arbitrary constant C is added to every result, because the derivative of a constant is zero. Any row can be checked by differentiating its right side.
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